Seminar history    

Dec 19 Thu Kok Leng Yeo (Max Planck Institute for Solar System Research, MPS) SP2RC seminar
The variation in solar irradiance is commonly assumed to be driven by its surface magnetism. Until recently, this assumption could not be verified conclusively as models of solar irradiance variability based on solar surface magnetism have to be calibrated to solar irradiance measurements. Making use of realistic three-dimensional magnetohydrodynamic simulations of the solar atmosphere and state-of-the-art full-disk magnetograms from SDO, we developed a model of total solar irradiance (TSI) that does not require any such calibration. The modelled TSI variability is therefore, unlike preceding models, independent of TSI measurements. The model replicates over 95% of the observed variability over the lifetime of SDO, confirming the relationship to solar surface magnetism and leaving limited scope for alternative drivers of solar irradiance variability (at least over the time scales examined, that is, days to years).

Dec 18 Wed Alexandr Buryak (Leeds) Algebra / Algebraic Geometry seminar
The WDVV equations, also called the associativity equations, is a system of non-linear partial differential equations for one function that describes the local structure of a Frobenius manifold. In enumerative geometry the WDVV equations control the Gromov-Witten invariants in genus zero. In his fundamental works, A. Givental interpreted solutions of the WDVV equations as cones in a certain infinite-dimensional vector space. This allowed him to introduce a group action on solutions of the WDVV equations which proved to be a powerful tool in Gromov-Witten theory. I will talk about a generalization of the Givental theory for the open WDVV equations that appeared in a work of A. Horev and J. Solomon in the context of open Gromov-Witten theory.

Dec 16 Mon Thomas Clay (Liverpool) Mathematical Biology Seminar Series

Dec 16 Mon Algebraic Geometry Learning Seminar

Dec 12 Thu James Cranch (Sheffield) Teaching Lunch
This summer, when I wasn't working in SoMaS as normal, I helped run the 60th International Mathematical Olympiad in Bath, and handed in a dissertation for a Masters degree in education. I'd like to talk about what these activities might have to do with one another: I'll speculate a bit about what universities can and should be doing to help school-aged students with their maths.

Dec 12 Thu Jeremy Colman (Sheffield) Statistics Seminar
SBC is a relatively new method for checking Bayesian inference algorithms. Its advocates (Talts et al. (2017)) argue that it identifies inaccurate computation and inconsistencies in model implementation and also provides graphical summaries to indicate the nature of the underlying problems. An example of such a summary is given. Although SBC has emerged from the Stan development team it is applicable to any Bayesian model that is capable of generating posterior samples. It does not require the use of any particular modelling language. I shall explain why there might indeed be a gap that SBC could fill, demonstrate how SBC works in practice, and discuss the balance between its costs and benefits.

Dec 12 Thu Gong Show Topology seminar

Dec 11 Wed Anitha Thillaisundaram (University of Lincoln) Pure Maths Colloquium
Groups of surfaces isogenous to a higher product of curves can be characterised by a purely group-theoretic condition, which is the existence of a so-called ramification structure. Gul and Uria-Albizuri showed that quotients of the periodic Grigorchuk-Gupta-Sidki groups, GGS-groups for short, admit ramification structures. We extend their result by showing that quotients of generalisations of the GGS-groups also admit ramification structures, with some deviations for the case p=2. This is joint work with Elena Di Domenico and Sukran Gul.

Dec 11 Wed Adeel Khan (University of Regensburg) Algebra / Algebraic Geometry seminar
I will discuss how various formalisms of intersection theory (Chow groups, K-theory, cobordism) can be extended to the setting of derived schemes and stacks. This gives a new approach to virtual phenomena such as the virtual fundamental class and virtual Riemann-Roch formulas.

Dec 11 Wed Theo Torres (University of Sheffield) Cosmology, Relativity and Gravitation
Wave scattering phenomena are ubiquitous in almost all Sciences, from Biology to Physics. Interestingly, it has been shown many times that different physical systems are the stage to the same processes. One stunning example is the observation that waves propagating on a flowing fluid effectively experience the presence of a curved space-time. In this talk we will use this analogy to investigate, both theoretically and experimentally, fundamental effects occurring around vortex flows and rotating black holes. In particular, we will focus on light-bending, superradiance scattering, and quasi-normal modes emission

Dec 11 Wed Callum Reader ShEAF: postgraduate pure maths seminar

Dec 10 Tue Sira Gratz (Glasgow) Algebra / Algebraic Geometry seminar
Classical frieze patterns are combinatorial structures which relate back to Gauss' Pentagramma Mirificum, and have been extensively studied by Conway and Coxeter in the 1970's.

A classical frieze pattern is an array of numbers satisfying a local (2 x 2)-determinant rule. Conway and Coxeter gave a beautiful and natural classification of SL(2)-friezes via triangulations of polygons. This same combinatorics occurs in the study of cluster algebras, and has revived interest in the subject. From this point of view, a natural way to generalise the notion of a classical frieze pattern is to ask of such an array to satisfy a (k x k)-determinant rule instead, for k bigger than 2, leading to the notion of higher SL(k)-friezes. While the task of classifying classical friezes yields a very satisfying answer, higher SL(k)-friezes are not that well understood to date.

In this talk, we'll discuss how one might start to fathom higher SL(k)-frieze patterns. The links between SL(2)-friezes and triangulations of polygons suggests a link to Grassmannian varieties under the Plücker embedding. We find a way to exploit this relation for higher SL(k)-friezes, and provide an easy way to generate a number of SL(k)-friezes via Grassmannian combinatorics, and suggest some ideas towards a complete classification using the theory of cluster algebras. This talk is based on joint work with Baur, Faber, Serhiyenko and Todorov.

Dec 10 Tue Jessica Fintzen (Cambridge) Number Theory seminar
The Langlands program is a far-reaching collection of conjectures that relate different areas of mathematics including number theory and representation theory. A fundamental problem on the representation theory side of the Langlands program is the construction of all (irreducible, smooth, complex) representations of p-adic groups. I will provide an overview of our understanding of the representations of p-adic groups, with an emphasis on recent progress. I will also briefly discuss applications to other areas, e.g. to automorphic forms and the global Langlands program.

Dec 9 Mon Yirui Xiong Algebraic Geometry Learning Seminar

Dec 6 Fri Yirui Xiong (Sheffield) Algebraic Geometry Learning Seminar

Dec 5 Thu Jeroen Sijsling (Ulm) Number Theory seminar
Algebraic curves over number fields play an important role in arithmetic geometry, for example in the proof by Andrew Wiles of the modularity Theorem, which uses elliptic curves. A very useful object for the study of more general algebraic curves is its Jacobian, because this abelian variety has a more linear structure than the curve itself. This talk describes how one can calculate with Jacobians in computer algebra systems. Many of these techniques use analytic approximations, in which case it is important to certify the correctness of such results. We discuss current algorithms for:
  • Calculating endomorphism rings of Jacobians;
  • Decomposing Jacobians into simple factors; and
  • Reconstructing curves from period matrices.

Dec 5 Thu Maria Carmen Reguera (University of Birmingham) Pure Maths Colloquium
Sparse operators are positive dyadic operators that have very nice boundedness properties. The L^p bounds and weighted L^p bounds with sharp constant are easy to obtain for these operators. In the recent years, it has been proven that singular integrals (cancellative operators) can be pointwise controlled by sparse operators. This has made the sharp weighted theory of singular integrals quite straightforward. The current efforts focus in understanding the use of sparse operators to bound rougher operators, such as oscillatory integrals. Following this direction, our goal in this talk is to describe the control of Bochner-Riesz operators by sparse operators.

Dec 5 Thu POSTPONED: Heather Battey (Imperial) Statistics Seminar

Dec 5 Thu Ieke Moerdijk (Utrecht/Sheffield) Topology seminar
As a digression from (and sufficiently independently of) the course on configuration spaces, I will explain Graeme Segal's proof that configuration spaces with labels in a pointed space $X$ model $\Omega^n \Sigma^n X$.

Dec 5 Thu Tom Van Doorsselaere (Centre for Mathematical Plasma-Astrophysics, KU Leuven ) Plasma Dynamics Group
In this seminar, I will discuss several aspects of waves in pores. These concentrations of magnetic field similar to miniature sunspots are wave guides for MHD waves. In contrast to waves in coronal loops, they are resolved across the wave guide, but it is harder to know what happens further along the magnetic field. I will discuss mode identification by using wave amplitude ratios, calculation of their energy fluxes as could be used for coronal heating, and resonant absorption of slow waves. An outlook to future work is also included.

Dec 4 Wed 1. Farhad Allian / 2. Hope Thackray (SoMaS) Applied Mathematics Colloquium
1. Coronal loop arcades form the building blocks of the hot and dynamic solar atmosphere. In particular, their oscillations serve as an indispensable tool in estimating the physical properties of the local environment by means of seismology. However, due to the nature of the arcade's complexity, these oscillations can be difficult to analyze. In this talk, I will present a novel image-analysis procedure based on the spatio-temporal autocorrelation function that can be utilized to reveal 'hidden' periodicities within EUV imagery of complex coronal loop systems. 2. Coronal loop models have often been used as a diagnostic tool for plasma properties in the Sun's corona. In particular, the oscillations triggered by nearby eruptive events may be modelled with a 3D semi-cylindrical waveguide. We investigate the resulting eigenfunctions for a “two-shell” (and later “three-shell”) density profile model that introduces sharp density contrast. We find that waves are elliptically polarised, but the eigenmodes can differ significantly when considering small changes to density profile. Such behaviour necessitates careful choice of density structure for understanding observational data.

Dec 4 Wed Natalie Hogg (University of Portsmouth) Cosmology, Relativity and Gravitation
There are well-known problems within the LambdaCDM model of cosmology, such as the H0 tension, that motivate the search for alternative dark energy models. In this talk, I will present one such alternative, known as the interacting vacuum scenario. In this scenario, the vacuum is free to exchange energy with the cold dark matter. Models of this type have the potential to resolve the H0 tension. I will start by discussing LCDM and its problems, then introduce the theory of the interacting vacuum model. I will present the results of a recent work (1902.10694) in which we constrained this model with observational data and conclude with a model comparison between the interacting model and LCDM.

Dec 3 Tue Dimitri Wyss (École Polytechnique Fédérale de Lausanne) Algebra / Algebraic Geometry seminar
Based on mirror symmetry considerations, Hausel and Thaddeus conjectured an equality between 'stringy' Hodge numbers for moduli spaces of $SL_n$/$PGL_n$ Higgs bundles. With Michael Groechenig and Paul Ziegler we prove this conjecture using non-archimedean integrals on these moduli spaces, building on work of Denef-Loeser and Batyrev. This approach reduces their conjecture essentially to the duality between generic Hitchin fibers. Similar ideas also lead to a new proof of the geometric stabilization theorem for anisotropic Hitchin fibers, a key ingredient in the proof of the fundamental lemma by Ngô. In my talk I will outline the main arguments of the proofs and discuss the adjustments needed, in order to replace non-archimedean integrals by motivic ones. The latter is joint work with François Loeser.

Dec 2 Mon Katrina Lythgoe (Oxford) Mathematical Biology Seminar Series

Nov 28 Thu Fionnlagh Mackenzie-Dover (SP2RC/Sheffield)

Nov 28 Thu POSTPONED: Marcel Ortgiese (Bath) Statistics Seminar

Nov 22 Fri Barbara Bolognese (Sheffield) Algebraic Geometry Learning Seminar

Nov 22 Fri Eleonora Di Valentino (University of Manchester) Cosmology, Relativity and Gravitation
The Cosmic Microwave Background (CMB) temperature and polarization anisotropy measurements from the Planck mission have provided a strong confirmation of the LCDM model of structure formation. However, there are a few interesting tensions with other cosmological probes and anomalies in the data that leave the door open to possible extensions to LCDM. The most famous ones are the Hubble constant and the S8 parameter tensions, the Alens anomaly and a curvature of the Universe. I will review all of them, showing some interesting extended cosmological scenarios, in order to find a new concordance model that could explain the current cosmological data.

Nov 21 Thu Julius Koza (Astronomical Institute, Slovak Academy of Sciences) SP2RC seminar
Flare loops form an integral part of eruptive events, being detected in the range of temperatures from X-rays down to cool chromospheric-like plasmas. While the hot loops are routinely observed by the Solar Dynamics Observatory’s Atmospheric Imaging Assembly, cool loops seen off-limb are rare. In this paper we employ unique observations of the SOL2017-09-10T16:06 X8.2-class flare which produced an extended arcade of loops. The Swedish 1 m Solar Telescope made a series of spectral images of the cool off-limb loops in the Ca II 8542 Å and the hydrogen H-beta lines. Our focus is on the loop apices. Non-LTE spectral inversion (non-LTE; i.e., departures from LTE) is achieved through the construction of extended grids of models covering a realistic range of plasma parameters. The Multilevel Accelerated Lambda Iterations (MALI) code solves the non-LTE radiative-transfer problem in a 1D externally illuminated slab, approximating the studied loop segment. Inversion of the Ca II 8542 Å and H-beta lines yields two similar solutions, both indicating high electron densities around 2x10^12 cm^(-3) and relatively large microturbulence around 25 km/s. These are in reasonable agreement with other independent studies of the same or similar events. In particular, the high electron densities in the range 10^12 - 10^13 cm^(-3) are consistent with those derived from the Solar Dynamics Observatory’s Helioseismic and Magnetic Imager white-light observations and they are also required to explain SST/CHROMIS continuum observations in the wide-band channel centered at 4845.5 Å.

Nov 21 Thu Soheyla Feyzbakhsh (Imperial College London) Algebra / Algebraic Geometry seminar
A classical method to study Brill-Noether locus of higher rank semistable vector bundles on curves is to examine the stability of coherent systems. To have an abelian category we enlarge the category of coherent systems by the category $A(C)$ which consists of triples $(E_1, E_2, f)$ where $E_1$ is a direct sum of the structure sheaf of $C, E_2$ is a coherent sheaf on $C$, and $f$ is a sheaf morphism from $E_1$ to $E_2$. In this talk after a short description of the derived category of $A(C)$, I will describe a 2-dimensional slice of the space of Bridgeland stability conditions on this category and sketch some of the possible applications of wall-crossing in Brill-Noether theory.

Nov 21 Thu Leo Bastos (LSHTM) Statistics Seminar
One difficulty for real-time tracking of epidemics is related to reporting delay. The reporting delay may be due to laboratory confirmation, logistic problems, infrastructure difficulties and so on. The ability to correct the available information as quickly as possible is crucial, in terms of decision making such as issuing warnings to the public and local authorities. A Bayesian hierarchical modelling approach is proposed as a flexible way of correcting the reporting delays and to quantify the associated uncertainty. Implementation of the model is fast, due to the use of the integrated nested Laplace approximation (INLA). The approach is illustrated on dengue fever incidence data in Rio de Janeiro, and Severe Acute Respiratory Illness (SARI) data in Paraná state, Brazil.

Nov 21 Thu Abigail Linton (Southampton) Topology seminar
A moment-angle complex $\mathcal{Z}_\mathcal{K}$ is obtained by associating a product of discs and circles to each simplex in a simplicial complex $\mathcal{K}$ and gluing these products according to how the corresponding simplices intersect. These spaces can have a complicated topological structure. For example, Baskakov (2003) found examples of non-trivial Massey products in the cohomology of moment-angle complexes. I will give a complete combinatorial classification of lowest-degree non-trivial triple Massey products in the cohomology of moment-angle complexes and describe constructions of simplicial complexes that give non-trivial higher Massey products on classes of any degree.

Nov 21 Thu Farhad Allian (Plasma Dynamics Group, University of Sheffield) Plasma Dynamics Group
Coronal loop arcades form the building blocks of the hot and dynamic solar atmosphere. In particular, their oscillations serve as an indispensable tool in estimating the physical properties of the local environment by means of seismology. However, due to the nature of the arcade's complexity, these oscillations can be difficult to analyze. In this talk, I will present a novel image-analysis procedure based on the spatio-temporal autocorrelation function that can be utilized to reveal 'hidden' periodicities within EUV imagery of complex coronal loop systems.

Nov 20 Wed Jan Spakula (University of Southampton) Pure Maths Colloquium

Let X be a countable discrete metric space, and think of operators on $\ell^2(X)$ in terms of their X-by-X matrix. Band operators are ones whose matrix is supported on a "band" along the main diagonal; all norm-limits of these form a C*-algebra, called uniform Roe algebra of X. This algebra "encodes" the large-scale (a.k.a. coarse) structure of X. Quasi-locality, coined by John Roe in '88, is a property of an operator on $\ell^2(X)$, designed as a condition to check whether the operator belongs to the uniform Roe algebra (without producing band operators nearby). The talk is about our attempt to make this work. (Joint with A Tikuisis and J Zhang.)

In the talk, I will introduce basics of coarse geometry, Property A and Roe algebras. Then I will move on to quasi-locality and (hopefully) the main ingredients of our argument: If X has Property A, then any quasi-local operator actually belongs to the Roe algebra.

Nov 20 Wed Dongho Chae (Chun-Ang) Applied Mathematics Colloquium
We consider the stationary Navier-Stokes equations in $ \Bbb R^{3}$ \begin{align} -\Delta u + (u \cdot \nabla) u = - \nabla p ,\quad \qquad\qquad \nabla \cdot u=0. \hspace{1cm}(1) \end{align} The standard boundary condition to impose at the spatial infinity is \begin{equation} u(x)\to 0 \quad \text{as} \quad |x|\to 0 . \hspace{4.5cm} (2) \end{equation} We also assume finiteness of the Dirichlet integral, \begin{equation} \int_{\Bbb R^3} |\nabla u|^2 dx <+\infty. \hspace{5cm} (3) \end{equation} Obviously $(u,p)$ with $u=0$ and $p=$constant is a trivial solution to (1)-(3). A very challenging open question is if there is another nontrivial solution. This Liouville type problem is wide open, and has been actively studied recently in the community of mathematical fluid mechanics. The explicit statement of the problem is written in Galdi's book [1][Remark X. 9.4, pp. 729], where under the stronger assumption $u\in L^{\frac{9}{2}} (\Bbb R^3)$ he concludes $u=0$. After that many authors deduce sufficient conditions stronger than (2) and/or (3) to obtain the Liouville type result. In this talk we review various previous results and present recent progresses in getting sufficient condition in terms of the potential functions of the velocity. We also show that similar method can applied to prove Liouville type theorems for the other related equations such as the magnetohydrodynamic equations(MHD), Hall-MHD and the non-Newtonian fluid equations.
  1. G. P. Galdi,: An introduction to the mathematical theory of the Navier- Stokes equations: Steady-State Problems, Springer, 2011.
  2. G. Seregin, Liouville type theorem for stationary Navier-Stokes equations, Nonlinearity, 29, (2016), pp. 2191-2195.
  3. D. Chae, Note on the Liouville type problem for the stationary Navier-Stokes equations in $\Bbb R^3$, J. Diff. Eqns, (in press)
  4. D. Chae and J. Wolf, On Liouville type theorem for the stationary Navier-Stokes equations, Calculus of Variations and PDEs, 58, (2019), no.3, 58:111.
  5. D. Chae and J. Wolf, On Liouville type theorems for the steady Navier-Stokes equations in $\Bbb R^3$, J. Diff. Eqns., 261, (2016), 5541-5560
  6. D. Chae, Liouville-type theorems for the forced Euler equations and the Navier-Stokes equations, Comm. Math. Phys., 326, (2014), pp. 37-48.

Nov 20 Wed Cesare Giulio Ardito (Manchester) ShEAF: postgraduate pure maths seminar
Donovan’s conjecture predicts that given a $p$-group $D$ there are only finitely many Morita equivalence classes of blocks of group algebras with defect group $D$. While the conjecture is still open for a generic $p$-group $D$, it has been proven in 2014 by Eaton, Kessar, Külshammer and Sambale when $D$ is an elementary abelian 2-group, and in 2018 by Eaton and Livesey when $D$ is any abelian 2-group. The proof, however, does not describe these equivalence classes explicitly. A classification up to Morita equivalence over a complete discrete valuation ring $\mathcal{O}$ has been achieved for $D$ with rank 3 or less, and for $D = (C_2)^4$. I have done $(C_2)^5$, and I have partial results on $(C_2)^6$. I will introduce the topic, give the relevant definitions and then describe the process of classifying this blocks, with a particular focus on the methodology and the individual tools needed to achieve a complete classification.

Nov 19 Tue Cathy Hsu (Bristol) Number Theory seminar
In his seminal work on modular curves and the Eisenstein ideal, Mazur studied the existence of congruences between certain Eisenstein series and newforms, proving that Eisenstein ideals associated to weight 2 cusp forms of prime level are locally principal. In this talk, we begin by discussing several generalizations of Mazur's results to squarefree levels, focusing primarily on the non-principality of the Eisenstein ideal in the anemic Hecke algebra associated to elliptic modular forms of weight 2 and trivial Nebentypus. We then discuss some work in progress, joint with Preston Wake and Carl Wang-Erickson, that establishes an algebraic criterion for having R=T in a certain non-Gorenstein setting.

Nov 19 Tue Jiawen Zhang (Southampton) Noncommutative Geometry Seminar

Roe algebras are C*-algebras associated to metric spaces, which encode their large scale structure. These algebras play a key role in higher index theory, bridging geometry, topology and analysis together. Recently we provide a new quasi-local perspective on Roe algebras, provided the underlying spaces have Yu’s Property A.

In the special case of a sequence of finite graphs, we study the quasi-locality of the averaging projection and introduce the notion of asymptotic expanders. Furthermore, we provide a structure theorem showing that asymptotic expanders can be ‘exhausted’ by classic expanders. Consequently, we show that asymptotic expanders cannot be coarsely embedded into any Hilbert space, and being asymptotic expanders can be detected via the Roe algebras.

This is a joint project with Ana Khukhro, Kang Li, Piotr Nowak, Jan Spakula and Federico Vigolo.

Nov 18 Mon Rastko Skepnek (Dundee) Mathematical Biology Seminar Series

Nov 18 Mon Anna Barbieri Algebraic Geometry Learning Seminar

Nov 14 Thu Greg Stevenson (Glasgow) Topology seminar
The aim of this talk is to give an introduction to what it might mean for a differential graded algebra (or ring spectrum) to be singular, in a sense analogous to the situation in algebraic geometry. As in geometry one can distinguish between smoothness and regularity, and I'll discuss both concepts and their relationship. The failure of the latter, i.e. the presence of singularities, can in good situations be described by a corresponding singularity category and time permitting I'll sketch how this category can be defined as in joint work with John Greenlees.

Nov 13 Wed Tom Morley (SoMaS) Applied Mathematics Colloquium
In General Relativity, the rate of expansion of the universe is governed by the cosmological constant. We know, from observations, that our universe is expanding at an accelerated rate, so the cosmological constant is usually taken to be positive. What happens if we choose the cosmological constant to be negative instead? Then we find ourselves in the weird and wonderful anti-de Sitter universe, a universe with a timelike boundary and closed timelike curves. And if we try to define a quantum field theory in this spacetime, we find some very surprising results indeed. In this talk, I will show how the vacuum polarisation, a divergent quantity associated with the local temperature of a quantum field, is affected by varying conditions imposed on the adS boundary.

Nov 11 Mon CANCELLED Statistics Seminar

Nov 11 Mon Nebojsa Pavic (Sheffield) Algebraic Geometry Learning Seminar

Nov 7 Thu Anwar Ali Aldhafeeri (Plasma Dynamics Group, University of Sheffield) SP2RC seminar
Many previous studies of MHD modes in the magnetic flux tubes were focussed on deriving a dispersion relation for cylindrical waveguides. However, from observations it is well known that, for example, the cross-sectional shape of sunspots and pores are not perfect circles and can often be much better approximated by ellipses. From a theoretical point of view, any imbalance in a waveguide’s diameters, even if very small, will move the study of the problem from cylindrical to elliptical coordinates. In this talk, I will therefore describe a model that predicts the MHD wave modes that can be trapped and propagate in a compressible magnetic flux tube with an elliptical cross-section embedded in a magnetic environment. I will discuss the resultant dispersion relations for body and surface modes, then then I will show how the ellipticity of a magnetic flux tube effects these solutions (with specific applications to the coronal and photospheric conditions). From a practical point of view the information from these dispersion diagrams does not show how these MHD modes will manifest themselves in observational data. Therefore, I will also present several visualisations of the eigenfunctions of these MHD wave modes and explain how the eccentricity effects each wave mode.

Nov 7 Thu Deborah Ashby (Imperial College London, President Royal Statistical Society) Statistics Seminar
The Royal Statistical Society was founded to address social problems ‘through the collection and classification of facts’, leading to many developments in the collection of data, the development of methods for analysing them, and the development of statistics as a profession. Nearly 200 years later an explosion in computational power has led, in turn, to an explosion in data. We outline the challenges and the actions needed to exploit that data for the public good, and to address the step change in statistical skills and capacity development necessary to enable our vision of a world where data are at the heart of understanding and decision-making.

Nov 7 Thu Emanuele Dotto (Warwick) Topology seminar
We will introduce the Witt vectors of a ring with coefficients in a bimodule and use them to calculate the components of the Hill-Hopkins-Ravenel norm for cyclic p-groups. This algebraic construction generalizes Hesselholt's Witt vectors for non-commutative rings and Kaledin's polynomial Witt vectors over perfect fields. We will discuss applications to the characteristic polynomial over non-commutative rings and to the Dieudonné determinant. This is all joint work with Krause, Nikolaus and Patchkoria.

Nov 7 Thu Norbert Magyar (University of Warwick) Plasma Dynamics Group
It is well known that in an infinite and homogeneous plasma, there are three types of waves: fast, slow, and Alfvén. However, richer dynamics appear in MHD once inhomogeneities are considered. The solar corona and solar wind is often seen to be highly structured, most probably even way below the current resolving capabilities of imaging instruments. The structuring of the plasma gives rise to some well-known phenomena such as surface and body modes, reflection/refraction of waves, phase mixing, resonant absorption and so on. The nonlinear implications of structuring are less well-known, though. In a series of numerical simulations, we will review the basic dynamics of waves supported by structures, and will connect these findings to the generation of turbulence in a structured plasma.

Nov 6 Wed Ana Khukhro (University of Cambridge) Pure Maths Colloquium
Expander graphs are somewhat contradictory geometric objects that have many applications, even outside of pure mathematics. We will see how they can be constructed with the help of geometric group theory, and how one can use some coarse-geometric variants of notions from topology to explore the world of resulting constructions.

Nov 6 Wed Nobert Magyar (Warwick) Applied Mathematics Colloquium
The solar corona and solar wind are still enigmatic from a physical standpoint. The coronal heating problem and the solar wind acceleration are one of the most important unsolved probems in astrophysics. Waves, which are omnipresent in the inner heliosphere, are strong candidates that might solve these conundrums. Just to make it even more difficult, the presence of waves might lead to the generation of turbulence, which is an unsolved problem on its own right. In this talk, we will explore what we know (and what we don't), first observationally and then by theory, about waves and turbulence in the extended solar corona. We will present the current magnetohydrodynamical (MHD) understading of turbulence generation in a plasma, which will be supplemented by my recent findings in the field.

Nov 6 Wed Lasse Schmieding (University of York) Cosmology, Relativity and Gravitation
Unlike higher dimensional de Sitter spaces, two dimensional de Sitter space is not simply connected. The behaviour of the fields on making a full rotation of the spatial direction must therefore be specified. Previously, Epstein and Moschella have shown that anti-periodic real scalar fields have no analogue of a Bunch-Davies vacuum state. For complex scalar fields, more general behaviour is possible. I will discuss complex scalar field theories in two dimensional de Sitter space and then comment on the existence of de Sitter invariant and Hadamard states for these theories. Along the way, I will review aspects of the representation theory of SL(2,R), the symmetry group relevant for two dimensional (anti-)de Sitter space.

Nov 6 Wed Eve Pound (Sheffield) ShEAF: postgraduate pure maths seminar
The Chevalley group is a subgroup of the automorphism group of a Lie algebra. In 1965, Iwahori and Matsumoto showed that, when the underlying field admits a nonarchimedean discrete valuation (for example, over Qp), these groups admit a double coset decomposition, or Bruhat decomposition. This decomposition allows lots of information about the group to be read off, and is intricately linked with the associated Bruhat-Tits building. In this talk, I'll start with the definition of a Lie algebra and try to motivate why we care about the Chevalley group, and give an overview of the geometric and combinatorial ideas in Iwahori and Matsumoto's work. If there is time, I will give some examples of how this links to buildings.

Nov 5 Tue Ben Davison (Edinburgh) Algebra / Algebraic Geometry seminar
I will discuss the positivity for quantum theta functions, a result of joint work with Travis Mandel: For a given skew-symmetric quantum cluster algebra, these functions provide a basis of a larger algebra, for which the structure constants are Laurent polynomials with positive coefficients. I will explain how the proof of this result follows from scattering diagram techniques and a very special case of the cohomological integrality theorem, joint work with Sven Meinhardt.

Nov 5 Tue Chris Nelson (QUB)

Nov 5 Tue Robert Kurinczuk (Imperial) Number Theory seminar
For general linear groups over a p-adic field, local Langlands in families (established recently by Helm-Moss) provides a description of the integral Bernstein centre in terms of rings of functions on moduli spaces of Galois representations. I will describe a conjectural generalization of this picture to all split reductive p-adic groups and, time permitting, I will discuss recent progress towards proving this conjecture. This is joint work with Jean-François Dat, David Helm, and Gil Moss.

Nov 4 Mon Adriana Dawes (Ohio State) Mathematical Biology Seminar Series

Nov 4 Mon Algebraic Geometry Learning Seminar

Oct 31 Thu Tom Hutchcroft (Cambridge) Statistics Seminar
Many questions in probability theory concern the way the geometry of a space influences the behaviour of random processes on that space, and in particular how the geometry of a space is affected by random perturbations. One of the simplest models of such a random perturbation is percolation, in which the edges of a graph are either deleted or retained independently at random with retention probability p. We are particularly interested in phase transitions, in which the geometry of the percolated subgraph undergoes a qualitative change as p is varied through some special value. Although percolation has traditionally been studied primarily in the context of Euclidean lattices, the behaviour of percolation in more exotic settings has recently attracted a great deal of attention. In this talk, I will discuss conjectures and results concerning percolation on the Cayley graphs of nonamenable groups and hyperbolic spaces, and give the main ideas behind our recent result that percolation in any transitive hyperbolic graph has a non-trivial phase in which there are infinitely many infinite clusters. The talk is intended to be accessible to a broad audience.

Oct 31 Thu Ai Guan (Lancaster) Topology seminar
Koszul duality is a phenomenon appearing in many areas of mathematics, such as rational homotopy theory and deformation theory. For differential graded (dg) algebras, the modern formulation of Koszul duality says there is a Quillen equivalence between model categories of augmented dg algebras and conilpotent dg coalgebras, and also Quillen equivalences between corresponding dg modules/comodules. I will give an overview of this circle of ideas, and then consider what happens when the conilpotence condition is removed. The answer to this question leads to an exotic model structure on dg modules that is "of second kind", i.e. weak equivalences are finer than quasi-isomorphisms. This is based on joint work with Andrey Lazarev from the recent preprint

Oct 30 Wed Natasha Morrison (University of Cambridge) Pure Maths Colloquium
One of the central objects of interest in additive combinatorics is the sumset $A + B := \{ a+b : a \in A, \, b \in B \}$ of two sets $A,B \subset \mathbb{Z}$. Our main theorem, which improves results of Green and Morris, and of Mazur, implies that the following holds for every fixed $\lambda > 2$ and every $k \ge (\log n)^4$: if $\omega \to \infty$ as $n \to \infty$ (arbitrarily slowly), then almost all sets $A \subset [n]$ with $|A| = k$ and $|A + A| \le \lambda k$ are contained in an arithmetic progression of length $\lambda k/2 + \omega$. This is joint work with Marcelo Campos, Mauricio Collares, Rob Morris and Victor Souza.

Oct 30 Wed Xin Huang (NAOC Beijing) Applied Mathematics Colloquium
Solar flares are intense flashes of radiation emanating from the Sun. A strong solar flare and it’s related eruptive events can interfere with high frequency radio communication, satellite operation, navigation equipment and so on. Furthermore, effects of solar flares could reach the earth within approximately 8 minutes. Therefore, solar flare forecast has caused long-term concern in the field of space weather. Solar flares originate from the release of the energy stored in the magnetic field of solar active regions, the triggering mechanism for these flares, however, remains unknown. Hence the statistical and machine learning methods are used to build the solar flare forecasting model. From the perspective of machine learning, we review the solar flare forecasting models and try to discuss the possible directions to build more powerful solar flare forecasting models.

Oct 30 Wed Thomas Stratton (University of Sheffield) Cosmology, Relativity and Gravitation
Since the direct detection of gravitational waves in 2015, a new window on the physical Universe has begun to open. A region of spacetime with large enough curvature, such as a black hole or neutron star, may scatter a freely propagating gravitational wave. I will consider scattering of gravitational waves by a compact star modelled with a polytropic equation of state. Within the framework of perturbation theory, I calculate the differential scattering cross section and discuss the interference effects present, namely rainbow and glory scattering. I will show how the star’s properties, such as the equation of state, imprint themselves on the cross section, and compare our results with black hole scattering.

Oct 30 Wed Maram Alossaimi, Lewis Combes, & Yirui Xiong (Sheffield) ShEAF: postgraduate pure maths seminar
Poisson Algebra
The concept of a Poisson algebra comes from defining a bilinear product {·, ·} on a commuta- tive algebra over a field K to bring a new non-commutative algebra structure. I will give some definitions, examples and the main Lemma in our research. In the end, if there is enough time I will introduce our new Poisson algebra structure.

An Introduction to the Theory of Elliptic Curve Cryptography
An elliptic curve over a finite field can be endowed with the structure of an abelian group. Within this group there are computations that are easy to perform, but hard to reverse. These computations form the basis of elliptic curve cryptography, an encryption standard with advantages and disadvantages when compared to traditional RSA methods. The downsides are such that an intimate understanding of certain mathematical properties of the chosen elliptic curve is needed to keep the protocol secure. In this talk I will go through the theory behind using elliptic curves for encryption, as well as some of the mathematical considerations that should be made when designing such a system.

Calabi-Yau algebras and superpotentials
Calabi-Yau algebras arise from transporting the conception of Calabi-Yau manifolds to noncommutative geometry, and now have profound applications in algebraic geometry and representation theory. One of the central problems in the study of Calabi-Yau algebras is their structural problem: can Calabi-Yau algebras be derived from superpotentials? We will review the answers to the problem based on work in the past years. And if time is permitted, I will introduce some applications based on structural theorems of Calabi-Yau algebras.

Oct 29 Tue Noah Arbesfeld (Imperial College London) Algebra / Algebraic Geometry seminar
Tautological bundles on Hilbert schemes of points often enter into enumerative and physical computations. I'll explain how to use the Donaldson-Thomas theory of threefolds to produce certain combinatorial identities involving Young diagrams. The resulting identities can be expressed geometrically in terms of tautological bundles over the Hilbert scheme of points on the plane. I'll also explain how these identities can be used to study Euler characteristics of tautological bundles over Hilbert schemes of points on general surfaces.

Oct 29 Tue Robertus (Sheffield)

Oct 28 Mon Jeremy Oakley (Sheffield) Statistics Seminar

Oct 28 Mon Algebraic Geometry Learning Seminar

Oct 24 Thu Petros Syntelis (Solar and Magnetospheric Theory Group, University of St Andrews) SP2RC seminar
Some of the most dynamic solar phenomena occur in complex magnetic configurations such as quadrupolar regions. To study eruptivity in quadrupolar regions, we perform 3D magnetohydrodynamic simulations of the partial emergence of two segments of a flux tube from the solar interior into a non-magnetized, stratified atmosphere. The emergence leads to the formation of two initially separated bipoles, which later come in contact, forming a strong polarity inversion line. Above the two bipoles, two magnetic lobes expand and interact through a series of current sheets at the interface between them. Two recurrent confined eruptions are produced. In both cases, the reconnection between sheared, low-lying field lines forms a flux rope. The confined eruptions result from the interaction between the two magnetic lobes at different heights in the solar atmosphere. These interactions create field lines that assist the eruption of the flux ropes, and also create other field lines that inhibit the eruptions. The flux rope of the first, weaker, eruption almost fully reconnects with the overlying field. The flux rope of the second, more energetic, eruption is confined by the overlying strapping field. During the second eruption, the flux rope is enhanced in size, flux, and twist, similar to confined-flare-to-flux-rope observations. Proxies of the emission reveal the two erupting filaments channels. A flare arcade is only formed in the second eruption owing to the longer lasting and more efficient reconnection at the current sheet below the flux rope.

Oct 24 Thu Frazer Jarvis (Sheffield) Teaching Lunch
New module approval forms have a strong recommendation that proposers should refer to 'Bloom's Taxonomy' when preparing their submissions. In this talk, we will discuss what this is, its history, and what it means in practice.

Oct 24 Thu Lyudmila Mihaylova (Sheffield) Statistics Seminar
We are experiencing an enormous growth and expansion of data provided by multiple sensors. The current monitoring and control systems face challenges both in processing big data and making decisions on the phenomena of interest at the same time. Urban systems are hugely affected. Hence, intelligent transport and surveillance systems need efficient methods for data fusion, tracking and prediction of individual vehicular traffic and aggregated flows. This talk will focus on two main methods able to solve such monitoring problems, by fusing multiple types of data while dealing with nonlinear phenomena – sequential Markov Chain Monte Carlo (SMCMC) methods with adaptive subsampling and Gaussian Process regression methods. The first part of this talk will present a SMCMC approach able to deal with massive data based on adaptively subsampling the sensor measurements. The main idea of the method to approximate the logarithm of the likelihood ratio by performing a trade-off between complexity and accuracy. The approach efficiency will be demonstrated on object tracking tasks. Next, Gaussian Process methods will be presented – for point and extended object tracking, i.e. both in space and in time. Using the derivatives of the Gaussian Process leads to an efficient replacement of multiple models that usually are necessary to represent the whole range of behaviour of a dynamic system. These methods give the opportunity to assess the impact of uncertainties, e.g. from the sensor data on the developed solutions.

Oct 24 Thu Richard Hepworth (Aberdeen) Topology seminar
Homological stability is a topological property that is satisfied by many families of groups, including the symmetric groups, braid groups, general linear groups, mapping class groups and more; it has been studied since the 1950's, with a lot of current activity and new techniques. In this talk I will explain a set of homological stability results from the past few years, on Coxeter groups, Artin groups, and Iwahori-Hecke algebras (some due to myself and others due to Rachael Boyd). I won't assume any knowledge of these things in advance, and I will try to introduce and motivate it all gently!

Oct 24 Thu Yuyang Yuan (Sheffield) Plasma Dynamics Group
In this talk I will explain and demonstrate the Solar Spicule Tracking Code (SSTC) that I have developed. This code has the ability to automatically detect and track the motion spicules in imaging data. I will specifically demonstrate the code working with images obtained using the H alpha line from the CRisp Imaging SpectroPolarimeter (CRISP) based at the Swedish Solar Telescope.

Oct 23 Wed Takashi Sakajo (Kyoto/INI Cambridge) Applied Mathematics Colloquium
We have investigated a mathematical theory classifying the topological structures of streamline patterns for 2D incompressible (Hamiltonian) vector fields on surfaces such as a plane and a spherical surface, in which a unique combinatorial structure, called partially Cyclically Ordered rooted Tree (COT), associated with a symbolic expression (COT representation) is assigned to every streamline topology. With the COT representations, one can identify the topological streamline structures without ambiguity and predict the possible transition of streamline patterns with a mathematical rigor. In addition, we have recently developed a software converting the values of stream function on structured/non-structured grid points in the plane into the COT representation automatically. It enables us to conduct the classification of streamline topologies for a large amount of flow datasets and the snapshots of time-series of flow evolutions obtained by measurements and numerical simulations, which we call Topological Flow Data Analysis (TFDA). The combinatorial classification theory of flow topologies is now extended to the flow of finite type, which contains Morse-Smale vector fields, compressible flows and 2D slices of 3D vector fields. I will present an overview of basic theory and its applications to atmospheric data and engineering problem.

Oct 23 Wed Joseph Martin (Sheffield) ShEAF: postgraduate pure maths seminar
The aim is to provide much of what is needed to understand the relationship between low-dimensional degenerate n-categories and their counterparts in the Periodic Table of n-categories. We first seek to establish a good understanding of equivalences between categories via a thorough study of adjunctions. Then we give an overview of the structures that can be found in the Periodic Table along with a useful result in each case. Finally, this is followed by an inspection of degenerate categories and bicategories, in particular we compare their totalities to that of monoids.

Oct 22 Tue Nick Sheridan (Edinburgh) Algebra / Algebraic Geometry seminar
I'll start by explaining a new method of computing asymptotics of period integrals using tropical geometry, via some concrete examples. Then I'll use this method to give a geometric explanation for a strange phenomenon in mirror symmetry, called the Gamma Conjecture, which says that mirror symmetry does not respect integral cycles: rather, the integral cycles on a complex manifold correspond to integral cycles on the mirror multiplied by a certain transcendental characteristic class called the Gamma class. We find that the appearance of zeta(k) in the asymptotics of period integrals arises from the codimension-k singular locus of the SYZ fibration.

Oct 22 Tue Fionnlagh Mackenzie-Dover (SP2RC/Sheffield)

Oct 22 Tue Thanasis Bouganis (Durham) Number Theory seminar
The properties (analytic, algebraic or p-adic) of special values of the standard L-function attached to Siegel and Hermitian modular forms are of central interest and have been extensively studied. In this talk, we will discuss another family of modular forms, which are associated to the isometry group of a quaternionic skew hermitian form. There are many similarities to the Siegel and Hermitian case but also important differences. We will present some results on the study of their standard L-function using the Rankin-Selberg method. This will lead us to discuss the existence of some theta series, a problem of which, in turn, is related to Howe duality and invariant theory.

Oct 21 Mon Raluca Eftimie (Dundee) Mathematical Biology Seminar Series

Oct 21 Mon Algebraic Geometry Learning Seminar

Oct 17 Thu Pierrick Bousseau (ETH Zurich) Algebra / Algebraic Geometry seminar
I will explain how to construct quasimodular forms starting from Betti numbers of moduli spaces of dimension 1 coherent sheaves on P2. This gives a proof of some stringy predictions about the refined topological string theory of local P2 in the Nekrasov-Shatashvili limit. Partly based on work in progress with Honglu Fan, Shuai Guo, and Longting Wu.

Oct 17 Thu Alexander Schenkel (Nottingham) Topology seminar
Algebraic quantum field theory (AQFT) is a well-established framework to axiomatize and study quantum field theories on Lorentzian manifolds, i.e. spacetimes in the sense of Einstein’s theory of general relativity. In the first part of the talk, I will try to explain both the physical context and the mathematical formalism of AQFT in a way that is hopefully of interest to topologists. In the second part of the talk, I will give an overview of our recent works towards establishing a higher categorical framework for AQFT. This will include the construction of examples of such higher categorical theories from (linear approximations of) derived stacks and a discussion of their descent properties.

Oct 16 Wed Haluk Sengun (Sheffield) Pure Maths Colloquium
The close relationship between index theory and representation theory is a classical theme. In particular, the trace formula has been studied through the lens of index theory by several researchers already. In joint work with Bram Mesland (Leiden) and Hang Wang (Shanghai), we take this connection further and obtain a formulation of the trace formula in K-theoretic terms. The central object here is the K-theory group of the C*-algebra associated to a locally compact group. This work is part of a program which explores the potential role that operator K-theory could play in the theory of automorphic forms.

Oct 16 Wed Nathan Johnson-McDaniel (Cambridge) Applied Mathematics Colloquium
Gravitational waves carry information directly to us from some of the most violent events in the universe, such as the mergers of binaries of black holes or neutron stars. Observations of such gravitational wave signals allow us to extract considerable information about the binaries that generate them. In particular, we can test whether general relativity (GR) is still a good description of gravity in such extreme situations. I will give an overview of the mathematics and statistics used in the analysis of gravitational wave data, from the analytical and numerical methods used to solve the field equations of GR and obtain model waveforms, to the Bayesian methods used to compare the data to these models. As an illustration, I will describe the tests of general relativity carried out on the compact binary signals detected by Advanced LIGO and Advanced Virgo during their first two observing runs. These tests did not reveal any deviation from the predictions of GR and have allowed us to put the most stringent constraints to date on possible deviations from these predictions in the strong field, highly dynamical regime.

Oct 15 Tue Jenny August (Max Planck Institute for Mathematics in Bonn) Algebra / Algebraic Geometry seminar
For a finite dimensional algebra, Bridgeland stability conditions can be viewed as a continuous generalisation of tilting theory, providing a geometric way to study the derived category. Describing this stability manifold is often very challenging but in this talk, I’ll look at a special class of symmetric algebras whose tilting theory is determined by a related hyperplane arrangement. This simple picture will then allow us to describe the stability manifold of such an algebra.

Oct 15 Tue Emma Gordon (Director of Administrative Data Research UK) Statistics Seminar
Administrative databases that are linked with each other or with survey data can allow deeper insights into the population’s life trajectories and needs and signal opportunities for improved and ultimately more personalised service delivery. Yet government agencies have to meet several prerequisites to realise these benefits. First among them is a stable legal basis. Appropriate laws and regulations have to exist to allow data merging within the limits of existing privacy protection. When different institutions are involved, these regulations have to clearly define each agencies’ responsibilities in collecting, safeguarding and analysing data. Second are technical requirements. This includes creating a safe infrastructure for data storage and analysis and developing algorithms to match individuals when databases do not share common unique personal identifiers. Third is the buy-in of the population. Public communication can highlight the value-added of linked databases and outline the steps taken to ensure data security and privacy. Involving citizens in dialogues about what data uses they are and are not comfortable with can help build public trust that appropriate limits are set and respected.

Oct 14 Mon Jeremy Oakley (Sheffield) Statistics Seminar
Discussion of Chapter 6 from "Deep Learning", by Goodfellow, Bengio and Courville

Oct 14 Mon George Moulantzikos, Evgeny Shinder Algebraic Geometry Learning Seminar

Oct 10 Thu Daniel Nóbrega-Siverio (Rosseland Centre for Solar Physics, University of Oslo) SP2RC seminar
Magnetic flux emergence from the solar interior has been shown to be a key mechanism for unleashing a wide variety of ejective and eruptive phenomena. However, there are still open questions concerning the role of different physical processes, like nonequilibrium (NEQ) ionization/recombination and the electrodynamics of partially ionized gases, in the rise of the magnetized plasma. Our aim is to investigate, for the first time, the impact of the NEQ formation of atomic and molecular hydrogen as well as the ambipolar diffusion term of the generalized Ohm’s law on the flux emergence process. This is possible through 2.5D flux emergence numerical experiments using the Bifrost code. In this presentation, we will report the first results of this research, emphasizing on the importance of having NEQ ionization to properly compute the effects of the ambipolar diffusion.

Oct 10 Thu Richard Glennie (St Andrews) Statistics Seminar
Distance sampling and spatial capture-recapture are statistical methods to estimate the number of animals in a wild population based on encounters between these animals and scientific detectors. Both methods estimate the probability an animal is detected during a survey, but do not explicitly model animal movement and behaviour. The primary challenge is that animal movement in these surveys is unobserved; one must average over all possible histories of each individual. In this talk, a general statistical model, with distance sampling and spatial capture-recapture as special cases, is presented that explicitly incorporates animal movement. An algorithm to integrate over all possible movement paths, based on quadrature and hidden Markov modelling, is given to overcome common computational obstacles. For distance sampling, simulation studies and case studies show that incorporating animal movement can reduce the bias in estimated abundance found in conventional models and expand application of distance sampling to surveys that violate the assumption of no animal movement. For spatial capture-recapture, continuous-time encounter records are used to make detailed inference on where animals spend their time during the survey. In surveys conducted in discrete occasions, maximum likelihood models that allow for mobile activity centres are presented to account for transience, dispersal, and heterogeneous space use. These methods provide an alternative when animal movement causes bias in standard methods and the opportunity to gain richer inference on how animals move, where they spend their time, and how they interact.

Oct 10 Thu Daniel Graves (Sheffield) Topology seminar
Homology theory for algebras was first introduced by Hochschild in the 40s to classify extensions of associative algebras. Since then a great many homology theories have been introduced to encode and detect desirable properties of algebras. I will describe a selection of these homology theories, discuss how they relate to one another and introduce some chain complexes for computing them.

Oct 10 Thu Anwar Aldhafeeri (Sheffield) Plasma Dynamics Group
The approach to understanding and analysing the behaviour of MHD we observed in the solar atmosphere is to find a relevant wave solution for the MHD equations. Therefore many previous studies focused on deriving a dispersion relation equation and solving this equation for a cylindrical tube. We know perfectly well that sunspots and pores do not have an ideal circular cross-section. Therefore, any imbalance in waveguide’s diameters, even if very small, will move the study of the problem from the cylindrical coordinates to elliptical coordinates. Thus the emphasis on knowing the properties and what type of wave modes exist in elliptical waveguides are much more critical than studying them in cylindrical coordinates. In this talk, I will start by deriving the dispersion relation in a compressible flux tube with elliptical cross-sectional shape. I will then solve the dispersion equation and discuss the solution of dispersion equation and how the ellipticity of tube effects the solutions with applications to coronal and photospheric conditions. However, the information we get from the dispersion diagram does not give the full picture of how we can observe a wave, and how much the wave mode changes when the cross-sectional shape of waveguide changes. Therefore I will present some visualisations of eigenfunctions of MHD wave modes and explain how the eccentricity effects each MHD wave mode.

Oct 9 Wed Xenia de la Ossa (University of Oxford) Pure Maths Colloquium
The mathematical structure of quantum moduli spaces in string theory contains a wealth of information about the physical behaviour of the effective field theories. However, research in this area has also lead to very interesting new mathematical structures. In this seminar I will describe new geometrical structures appearing in the context of “heterotic strings” associated to gauge bundles on manifolds with certain special structures. We will see how to recast these geometric systems in terms of the existence of a nilpotent operator and describe the tangent space to the moduli space. I will talk about a number of open problems, in particular, the efforts to understand higher order deformations, the global structure of the full moduli space, and the expectation of new dualities similar to mirror symmetry.

Oct 9 Wed Adam Moss (University of Nottingham) Cosmology, Relativity and Gravitation
I introduce a novel Bayesian inference tool that uses a neural network to parameterise efficient Markov Chain Monte-Carlo (MCMC) proposals. The target distribution is first transformed into a diagonal, unit variance Gaussian by a series of non-linear, invertible, and non-volume preserving flows. Neural networks are extremely expressive, and can transform complex targets to a simple latent representation from which one can efficiently sample. Using this method, I develop a nested MCMC sampler, finding excellent performance on highly curved and multi-modal analytic likelihoods. I also demonstrate it on Planck 2015 data, showing accurate parameter constraints, and calculate the evidence for simple one-parameter extensions to LCDM in $\sim20$ dimensional parameter space.

Oct 8 Tue Dhruv Ranganathan (Cambridge) Algebra / Algebraic Geometry seminar
The Gromov-Witten theory of a smooth variety X is a collection of invariants, extracted from the topology of the space of curves in X. I will explain how the Gromov-Witten theory of X can be computed algorithmically from the components of a simple normal crossings degeneration of X. The combinatorics of the geometry and complexity of the algorithm are both controlled by tropical geometry. The formula bears a strong resemblance to the Mayer-Vietoris sequence in elementary topology, and I will try to give some indication of how deep this analogy runs. Part of this story is still work in progress, joint with Davesh Maulik.

Oct 7 Mon Adel Betina, Evgeny Shinder Algebraic Geometry Learning Seminar

Oct 3 Thu Ulrich Pennig (Cardiff) Topology seminar
Twisted K-theory is a variant of topological K-theory that allows local coefficient systems called twists. For spaces and twists equipped with an action by a group, equivariant twisted K-theory provides an even finer invariant. Equivariant twists over Lie groups gained increasing importance in the subject due to a result by Freed, Hopkins and Teleman that relates the corresponding K-groups to the Verlinde ring of the associated loop group. From the point of view of homotopy theory only a small subgroup of all possible twists is considered in classical treatments of twisted K-theory. In this talk I will discuss an operator-algebraic model for equivariant higher (i.e. non-classical) twists over SU(n) induced by exponential functors on the category of vector spaces and isomorphisms. These twists are represented by Fell bundles and the C*-algebraic picture allows a full computation of the associated K-groups at least in low dimensions. I will also draw some parallels of our results with the FHT theorem. This is joint work with D. Evans.

Oct 2 Wed Bartek Protas (McMaster/INI Cambridge) Applied Mathematics Colloquium
In the presentation we will discuss our research program focused on a systematic search for extreme, potentially singular, behaviors in the Navier-Stokes system and in other models of fluid flow. Enstrophy and enstrophy-like quantities serve as convenient indicators of the regularity of solutions to such system -- as long as these quantities remains finite, the solutions are guaranteed to be smooth and satisfy the equations in the classical (pointwise) sense. However, there are no available estimates with finite a priori bounds on the growth of enstrophy in 3D Navier-Stokes flows and hence the regularity problem for this system remains open. While the 1D Burgers and the 2D Navier-Stokes system are known to be globally well posed, the question whether the corresponding estimates on the instantaneous and finite-time growth of various enstrophy-like quantities is quite relevant. We demonstrate how new insights concerning such questions can be obtained by formulating them as variational PDE optimization problems which can be solved computationally using suitable discrete gradient flows. More specifically, such an optimization formulation allows one to identify "extreme" initial data which, subject to certain constraints, leads to the most singular flow evolution which can then be compared with upper bounds obtained using rigorous methods of mathematical analysis. In order to quantify the maximum possible growth of enstrophy in 3D Navier-Stokes flows, we consider a family of such optimization problems in which initial conditions with prescribed enstrophy E_0 are sought such that the enstrophy in the resulting Navier-Stokes flow is maximized at some time T. By solving these problems for a broad range of values of E_0 and T, we demonstrate that the maximum growth of enstrophy is in fact finite and scales in proportion to E_0^{3/2} as E_0 becomes large. Thus, in such worst-case scenario the enstrophy still remains bounded for all times and there is no evidence for formation of singularity in finite time. We also analyze properties of the Navier-Stokes flows leading to the extreme enstrophy values and show that this behavior is realized by a series of vortex reconnection events.

Oct 2 Wed Peter Millington (University of Nottingham) Cosmology, Relativity and Gravitation
The non-rotating fermion vacuum in Kerr spacetimes is unstable to a spontaneous vacuum decay, which leads to the formation of a co-rotating Dirac sea. This decay, which amounts to the fermionic pendant of the black hole bomb instability, has an analogue in the electrodynamics of supercritical fields, and we show that the decay process is encoded by the set of quasi-normal fermion modes.

Oct 1 Tue Paul Johnson (Sheffield) Algebra / Algebraic Geometry seminar
This will be a gentle, expository talk explaining some connections between the two objects in the title. I will begin with partitions: using the cores-and-quotients formula to motivate the statement of an enriched version of Euler's product formula for partitions, that was conjectured by Gusein-Zade, Luengo, and Melle-Hernández in 2009, and that I proved this summer with Jørgen Rennemo. Most of the talk will be giving the geometric context for this combinatorial formula, namely how Gusein-Zade, Luengo and Melle-Hernández came to discover it by studying Hilbert schemes of points on orbifolds, and how to use Chen-Ruan cohomology to generalise it and connect it to existing results on Hilbert schemes. I will vaguely gesture toward the proof in the last five minutes for the experts, but most of the talk should be accessible to the whole audience.

Sep 30 Mon Evgeny Shinder (Sheffield) Algebraic Geometry Learning Seminar

Sep 17 Tue Francesco Sala (IPMU Tokyo) Algebra / Algebraic Geometry seminar
Let $\mathcal{M}$ denote the moduli stack of either coherent sheaves on a smooth projective surface or Higgs sheaves on a smooth projective curve $X$. The convolution algebra structure on the Borel-Moore homology of $\mathcal{M}$ is an instance of two-dimensional cohomological Hall algebras. These examples were defined by Kapranov-Vasserot and by Schiffmann and me, respectively. In the present talk, I will describe a full categorification of the cohomological Hall algebra of $\mathcal{M}$. This is achieved by exhibiting a derived enhancement of $\mathcal{M}$. Furthermore, this method applies also to several other moduli stacks, such as the moduli stack of vector bundles with flat connections on $X$ and the moduli stack of finite-dimensional representations of the fundamental group of $X$. In the curve case, we call the corresponding categorified algebras the Betti, de Rham, and Dolbeaut categorified Hall algebras of the curve $X$, respectively. In the second part of the talk, I will discuss some relations between these categorified Hall algebras. This is based on a joint work with Mauro Porta.

Sep 11 Wed Baofang Song (Center for Applied Mathematics, Tianjin University) Applied Mathematics Colloquium
The transition to turbulence in wall-bounded shear flows, such as pipe, channel, and Couette flows, is a fundamental problem of fluid dynamics. The questions of when and how turbulence rises in these flows, as Reynolds number increases, have challenged scientists and engineers for over a century and have not been fully understood till today. The complexity lies in the subcritical nature of the transition in these flows and the coexistence of various turbulent states and the quiescent laminar state during the transition process. Nevertheless, in recent years, significant advancements in this research area have been made. In this talk, I will present some results of our team on the transition to turbulence as well as turbulence control in pipe flow.

Aug 22 Thu Jason Green (Massachusetts Boston) Applied Mathematics Colloquium
Molecular motion in fluids is a consequence of well-known physical laws, but in diverse soft matter contexts, it is challenging to construct predictions of bulk properties directly from the nonlinear intermolecular forces. The difficulty is that molecules in liquids are constantly moving, in a perpetual state of collision and chaos. As a result, their dynamics sit balanced at the knife-edge between the sharp, well-defined collisions in gases and the ordered oscillations in crystalline solids. That is, the disordered liquid state reflects a tension between order and chaos. This tension is especially heightened at the liquid-vapor critical point where strong statistical correlations imply structural organization that is intrinsically opposed by the chaotic dynamics. The goal of this talk will be to explain some recent developments coupling nonlinear dynamics and statistical physics and how these advances are beginning to offer a mechanistic view of longstanding paradigms in liquid state theory and critical phenomena. Critical fluctuations and slowing down of chaos Moupriya Das, Jason R. Green Nat. Commun. 2019 10(1) p. 2155 Self-averaging fluctuations in the chaoticity of simple fluids Moupriya Das, Jason R. Green Phys. Rev. Lett. 2017 119(11), p. 115502 Extensivity and additivity of the Kolmogorov-Sinai entropy for simple fluids Moupriya Das, Anthony B. Costa, Jason R. Green Phys. Rev. E 2017 95(2), p. 022102

Aug 14 Wed Ben Evans (Bristol) Mathematical Biology Seminar Series
Part of the appeal of deep convolutional networks is their ability to learn on raw data, obviating the need to hand-code the feature space. It has been demonstrated that when networks perform "end- to-end" learning, they develop features in early layers that not only lead to a good classification performance but also resemble the representations found in biological vision systems. These results have been used to draw various parallels between deep learning systems and human visual perception. In this study, we show that end-to-end learning in standard convolutional neural networks (CNNs) trained on a modified CIFAR-10 dataset are found to rely upon idiosyncratic features within the dataset. Instead of relying on abstract features such as object shape, end-to-end learning can pick up on low-level and spatially high-frequency features, such as noise-like masks. Such features are extremely unlikely to play any role in human object recognition, where instead a strong preference for shape is observed. Through a series of empirical studies, we show that these CNNs cannot overcome such problems merely through regularisation methods or more ecologically plausible training regimes. However, we show that these problems can be ameliorated by forgoing end-to-end learning and processing images with Gabor filters in a manner that more closely resembles biological vision systems. These results raise doubts over the assumption that simply learning end-to-end in "vanilla" CNNs leads to the emergence of similar representations to those observed in biological vision systems. By adding more biological input constraints, we show that deep learning models can not only capture more aspects of human visual perception, but also become more robust to idiosyncratic biases within training sets.

Jul 2 Tue Evgeny Shinder (Sheffield)

Jul 2 Tue Caitlin Buck (Sheffield)

Jul 2 Tue Neil Dummigan (Sheffield)

Jun 20 Thu Ioannis Kontogiannis (Leibniz-Institut für Astrophysik Potsdam, AIP)
We study the emergence and evolution of new magnetic flux in the vicinity of a quiet Sun network. We employ high-resolution spectropolarimetric, spectroscopic and spectral imaging observations from ground-based (Dutch Open Telescope) and space-born instruments (TRACE, Hinode, SoHO), which provided a multi-wavelength, tomographic view of the region from the photosphere up to the corona. Throughout its evolution, the region exhibited many of the phenomena revealed by recent simulations. The event starts with a series of granular-scale events, which follow the photospheric flow field and merge to form a small-scale magnetic flux system of the order of 1018 Mx. Spectropolarimetric inversions reveal an evolving, complicated pattern of horizontal and vertical magnetic field patches at the region between the main polarities. As the magnetic flux accumulates and the region expands, Doppler-shifted H-alpha absorption features appear above and at the crests of the structure, indicating an immediate interaction with the pre-existing, overlying magnetic field. Roughly 60 min after the region first emerged at the photosphere, a jet-like feature appeared in the chromosphere and a small soft X-ray bright point formed in the corona. The coronal brightening exhibited intense spatial and temporal variations and had a lifetime that exceeded one hour. EUV spectroscopy and DEM analysis revealed temperatures up to 106 K and densities up to 1010 cm-3. Even in the absence of a strong ambient magnetic field, small-scale magnetic flux emergence affects dramatically the dynamics and shape of the quiet Sun.

Jun 20 Thu Ioannis Kontogiannis (Leibniz-Institut für Astrophysik Potsdam, AIP) SP2RC seminar
We study the emergence and evolution of new magnetic flux in the vicinity of a quiet Sun network. We employ high-resolution spectropolarimetric, spectroscopic and spectral imaging observations from ground-based (Dutch Open Telescope) and space-born instruments (TRACE, Hinode, SoHO), which provided a multi-wavelength, tomographic view of the region from the photosphere up to the corona. Throughout its evolution, the region exhibited many of the phenomena revealed by recent simulations. The event starts with a series of granular-scale events, which follow the photospheric flow field and merge to form a small-scale magnetic flux system of the order of 1018 Mx. Spectropolarimetric inversions reveal an evolving, complicated pattern of horizontal and vertical magnetic field patches at the region between the main polarities. As the magnetic flux accumulates and the region expands, Doppler-shifted H-alpha absorption features appear above and at the crests of the structure, indicating an immediate interaction with the pre-existing, overlying magnetic field. Roughly 60 min after the region first emerged at the photosphere, a jet-like feature appeared in the chromosphere and a small soft X-ray bright point formed in the corona. The coronal brightening exhibited intense spatial and temporal variations and had a lifetime that exceeded one hour. EUV spectroscopy and DEM analysis revealed temperatures up to 106 K and densities up to 1010 cm-3. Even in the absence of a strong ambient magnetic field, small-scale magnetic flux emergence affects dramatically the dynamics and shape of the quiet Sun.

Jun 18 Tue Tong Liu (Purdue) Number Theory seminar
Let K be a p-adic field, it is known that p-adic Tate module of p-divisible group over O_K is crystalline representation with Hodge-Tate weights in [0, 1]. And conversely any such crystalline representation arise from a p-divisible group over O_K. In this talk, we discuss how to generalize this result to relative bases when O_K is replaced by more general rings, like, Z_p[[t]]. This is a joint work with Yong Suk Moon.

Jun 11 Tue Andreas Krug (Magburg) Algebra / Algebraic Geometry seminar
Given a vector bundle E over smooth variety X, there is a natural way to associate a vector bundle, called tautological bundle, on the Hilbert scheme of points on X. In this talk, we will discuss stability of tautological bundles in the case that X is a curve.

May 31 Fri Prof Yuanyong Deng (Director of Huairoi Observatory) (NAOC, CAS, China) SP2RC seminar
In this presentation I will briefly introduce recent solar observation and related research in China. Up to now all these observations come from ground-based telescopes. In the near future, Chinese will have our first space solar observatory by the Advanced Space solar telescope (ASO-S). In addition to ASO-S, some other projects under development or proposed will also be introduced and discussed.

May 30 Thu David Jess (Queen's University (Belfast)) Plasma Dynamics Group
The solar atmosphere provides a unique astrophysical laboratory to study the formation, propagation, and subsequent dissipation of magnetohydrodynamic (MHD) waves across a diverse range of spatial scales. The concentrated magnetic fields synonymous with sunspots allow the examination of guided magnetoacoustic modes as they propagate upwards into the solar corona, where they exist as ubiquitous 3-minute waves readily observed along loops, plumes and fan structures. While cutting-edge observations and simulations are providing insights into the underlying wave generation and damping mechanisms, the in-situ amplification of magnetoacoustic waves as they propagate through the solar chromosphere has proved difficult to explain. Here we provide observational evidence of a resonance cavity existing above a magnetic sunspot, where the intrinsic temperature stratification provides the necessary atmospheric boundaries responsible for the resonant amplification of these waves. Through comparisons with high-resolution numerical MHD simulations, the geometry of the resonance cavity is mapped across the diameter of the underlying sunspot, with the upper boundaries of the chromosphere ranging between 1300–2300 km. This brings forth important implications for next-generation ground-based observing facilities, and provides an unprecedented insight into the MHD wave modelling requirements for laboratory and astrophysical plasmas.

May 17 Fri Gong Show Topology seminar

May 16 Thu Christopher Fallaize (Nottingham) Statistics Seminar
In shape analysis, objects are often represented as configurations of points, known as landmarks. The case where the correspondence between landmarks on different objects is unknown is called unlabelled shape analysis. The alignment task is then to simultaneously identify the correspondence between landmarks and the transformation aligning the objects. In this talk, I will discuss the alignment of unlabelled shapes, and discuss two applications to problems in structural bioinformatics. The first is a problem in drug discovery, where the main objective is to find the shape information common to all, or subsets of, a set of active compounds. The approach taken resembles a form of clustering, which also gives estimates of the mean shapes of each cluster. The second application is the alignment of protein structures, which will also serve to illustrate how the modelling framework can incorporate very general information regarding the properties we would like alignments to have; in this case, expressed through the sequence order of the points (amino acids) of the proteins.

May 16 Thu Peter Wyper (University of Durham) Plasma Dynamics Group
The majority of free energy in the solar corona is stored within sheared magnetic field structures known as filament channels. Filament channels spend most of their life in force balance before violently erupting. The largest produce powerful solar flares and coronal mass ejections (CMEs), whereby the filament channel is bodily ejected from the Sun. However, a whole range of smaller eruptions and flares also occur throughout the corona. Some are ejective, whilst others are confined. Recently it has been established that coronal jets are also typically the result of a filament channel eruption. The filament channels involved in jets are orders of magnitude smaller than the ones which produce CMEs. In this talk I will start by considering these tiny, jet producing eruptions. I will introduce our MHD simulation model that well describes them and then discuss what jets can tell us about solar eruptions in general. Specifically, I will argue that many different types of eruption can be understood by considering two defining features: the scale of the filament channel and its interaction via reconnection with its surrounding magnetic topology.

May 15 Wed Martina Balagovic (Newcastle) Pure Maths Colloquium

The quantum Yang Baxter equation arose in statistical mechanics around 1970 as the consistency condition for an interaction of two particles on a line. In the 1980s, Drinfled and Jimbo introduced quantum groups (deformations of universal enveloping algebras of Lie algebras), and showed that they allow a universal R matrix - an element constructed from the algebra, which systematically produces a solution of the quantum Yang Baxter equation in every representation of this algebra. In turn, this imposes a structure of a braided tensor category on representations of the quantum group (i.e. gives an action of the braid group of type A) and leads to the Reshetikhin-Turaev construction of invariants of knots, braids, and ribbons.

Considering the same problem with a boundary (on a half line instead of a line) leads to the consistency condition called the (quantum) reflection equation, introduced by Cherednik and Sklyanin in the 1980s. I will explain how, in the joint work with S. Kolb, we use quantum symmetric pairs (Noumi, Sugitani, and Dijkhuizen; Letzter 1990s) to construct a universal K-matrix - an element which systematically produces solutions of the reflection equation. This gives an action of the braid group of type B, endowing the corresponding category of representations with a structure of a braided tensor category with a cylinder twist (as defined by T. tom Dieck, R. Haring-Oldenburg 1990s).

May 14 Tue Anna Krystalli / Alison Parton / Lyn Taylor (Sheffield / Sheffield / Phastar) RSS Seminar Series
R and its ecosystem of packages offers a wide variety of statistical and graphical techniques and is increasing in popularity as the tool of choice for data analysis in academia. In addition to its powerful analytical features, the R ecosystem provides a large number of tools and conventions to help support more open, robust and reproducible research. This includes tools for managing research projects, building robust analysis workflows, documenting data and code, testing code and disseminating and sharing analyses. In this talk we’ll take a whistle-stop tour of the breadth of available tools, demonstrating the ways R and the Rstudio integrated development environment can be used to underpin more open reproducible research and facilitate best practice.

R has cemented itself as the language of choice for many a statistician and data scientist, but is often heckled as a sluggish competitor to the likes of python. This talk will discuss one avenue for maintaining the comfort and power of R (see Anna’s talk!) without having to wait days for your desktop analysis to complete. The foreach package is a set of functions that allow virtually anything that can be expressed as a for-loop as a set of parallel tasks. By registering a parallel backend through the doParallel package, you can speed up the run-time of your work by utilising the full capacity of your machine. I’ll introduce how to rewrite workflows to utilise the foreach approach and show how you can implement a parallel workflow on your own machine with doParallel. For a low-range machine, this will reduce your run-time by 4-fold and for those lucky few with high-range budgets you’ll receive something around 16-fold. So how about going one step further, and increasing to hundreds-fold? We can achieve this by using cloud computing services, taking the load away from your own machine. Cloud computing services have been seen to have a steep learning curve and this has led to many shying away from using such a useful resource. I’ll introduce you to the doAzureParallel package for R, create by Microsoft to bypass this learning curve and allow you to implement the foreach package in parallel in the cloud with only minor amendments to the R code that has been blighting you for months.

To date, the use of R Software in the pharmaceutical industry has been relatively limited to exploratory work and not routinely used in regulatory submissions where SAS® Software is still favored. One of the difficulties in using R for submissions is being able to provide the regulators with appropriate documentation of testing and validation for the packages used. In June 2018 the R consortium granted funding for a PSI AIMS SIG initiative to create an online ‘R package validation repository’. With representatives from Abbvie, Amgen, Biogen, Eli Lilly, FDA, GSK, J&J, Merck, Merck KGaA, Novartis, PPD, PRA, Pfizer, Roche / Genentech, Syne qua non and the Transcelerate project, the ‘R Validation Hub’ team launched a free to access web site to host validation documentation and metrics for R packages ( Although, the project is still in its early stages, we are looking to expand on the website content and encourage contribution of R metrics and tests for packages from all R-users. The talk will discuss what is meant by validation, how R differs to SAS, justify our approach to the validation issue and present the future capabilities of the website and how all R-users are set to benefit from the work.

May 13 Mon Natasha Ellison, Sara Hilditch, Elena Marensi, Alison Parton, Lizzie Sheppeck, Sarah Whitehouse, Sadiah Zahoor (University of Sheffield) International Women in Mathematics Day

May 13 Mon Suzana de Souza e Almeida Silva (Technological Institute of Aeronautics, Sao Paulo) Plasma Dynamics Group
Lagrangian coherent structures (LCS) is a newly developed theory which describes the skeleton of turbulent flows. LCS act as barriers in the flow, separating regions with different dynamics and organizing the flow into coherent patterns. This talk will introduce some concepts of LCT techniques as well as recent application to solar physics problems.

May 13 Mon Yuri M. Pismak (St. Petersburg State University) Applied Mathematics Colloquium
The method proposed by K. Symanzik for constructing quantum field models in an inhomogeneous space-time is used to describe the interaction of the quantum electrodynamics (QED) fields with material objects. It is carried out within the framework of quantum field models in which the QED Lagrangian is modified according to the QED basic principles (locality, gauge invariance, renormalizability) and taking into account the properties of the material medium interacting with QED fields. Models with interactions of electromagnetic and Dirac fields with two-dimensional materials of flat, spherical and cylindrical shape are considered. The results obtained in such models for the Casimir effect, scattering processes and bound states are discussed.

May 13 Mon Nuria Folguera Blasco (Crick Institute) Mathematical Biology Seminar Series

May 9 Thu Rebecca Killick (Lancaster) Statistics Seminar
Historically much of the research on changepoint analysis has focused on the univariate setting. Due to the growing number of high dimensional datasets there is an increasing need for methods that can detect changepoints in multivariate time series. In this talk we focus on the problem of detecting changepoints where only a subset of the variables under observation undergo a change, so called subset multivariate changepoints. One approach to locating changepoints is to choose the segmentation that minimises a penalised cost function via a dynamic program. The work in this presentation is the first to create a dynamic program specifically for detecting changes in subset-multivariate time series. The computational complexity of the dynamic program means it is infeasible even for medium datasets. Thus we propose a computationally efficient approximate dynamic program, SPOT. We demonstrate that SPOT always recovers a better segmentation, in terms of penalised cost, then other approaches which assume every variable changes. Furthermore under mild assumptions the computational cost of SPOT is linear in the number of data points. In small simulation studies we demonstrate that SPOT provides a good approximation to exact methods but is feasible for datasets that contain thousands of variables observed at millions of time points. Furthermore we demonstrate that our method compares favourably with other commonly used multivariate changepoint methods and achieves a substantial improvement in performance when compared with fully multivariate methods.

May 8 Wed Aditi Kar (Royal Holloway) Pure Maths Colloquium
I will discuss a conjecture about stabilisation of deficiency in finite index subgroups of a finitely presented group and relate it to the D2 Problem of C.T.C. Wall and the Relation Gap problem. I will explain a pro-p version of the conjecture, as well as its higher dimensional abstract analogues and why we can verify the conjecture in these cases.

May 8 Wed Kasia Rejzner (York) Applied Mathematics Colloquium
In this talk I will present recent results on the construction of the net of local algebras for the sine-Gordon model. The approach I will present is that of perturbative algebraic QFT, in which the interacting fields are constructed using formal S-matrices. It has been shown that in sine-Gordon model these formal S-matrices can be realized as unitary operators in certain Hilbert space representation, appropriate for massless scalar field in 2 dimensions.

May 3 Fri James Brotherston THH reading group

May 2 Thu Celeste Damiani (Leeds) Topology seminar

May 2 Thu Youra Taroyan (Aberystwyth University) Plasma Dynamics Group
Solar prominences are dense magnetic structures that are anchored to the visible surface known as the photosphere. They extend outwards into the Sun’s upper atmosphere known as the corona. Twists in prominence field lines are believed to play an important role in supporting the dense plasma against gravity as well as in prominence eruptions and coronal mass ejections (CMEs), which may have severe impact on the Earth and its near environment. We will use a simple model to mimic the formation of a prominence thread by plasma condensation. The process of coupling between the inflows and the twists will be discussed. We show that arbitrarily small magnetic twists should be amplified in time during the mass accumulation process. The growth rate of the twists is proportional to the mass condensation rate.

May 1 Wed Sam Falle (Leeds) Applied Mathematics Colloquium
In this talk I will consider shock structures that arise in systems of hyperbolic balance laws, i.e. hyperbolic systems of conservation laws with source terms. I show how the Whitham criterion for the existence of such shock structures can be extended to systems with more than one relaxation variable. In addition, I descibe a method based on the Hermite-Biehler theorem that is useful for determining the stability of the equilibrium states of such systems. The utility of this method is illustrated by a number of examples: ideal gas with two internal degrees of freedom, two fluid magnetohydrodynamics and magnetohydrodynamics with tensor resistivity.

May 1 Wed Esmee te Winkel (Warwick) ShEAF: postgraduate pure maths seminar
In geometric group theory, it is common to try to study a group by finding a meaningful action on a metric space. This talk is about the mapping class group of a compact surface and its action on various graphs. The mapping class group is the group of homeomorphisms up to isotopy. I will define this group and state some of its properties and open questions. After this motivation, I will introduce the curve graph and the pants graph associated to a surface and explain how the mapping class group acts on them.

Apr 18 Thu Philippa Browning (University of Manchester) Plasma Dynamics Group
In this talk, I will describe recent models of plasma heating and non-thermal particle acceleration in flares, focussing on the role of twisted magnetic flux ropes as reservoirs of free magnetic energy. First, using 2D magnetohydrodynamic simulations coupled with a guiding-centre test-particle code, I will describe magnetic reconnection and particle acceleration in a large-scale flaring current sheet, triggered by an external perturbation – the “forced reconnection” scenario. I will show how reconnection is involved both in creating twisted flux ropes, and in their merger, how this depends on the nature of the driving disturbance, and how particles are accelerated by the different modes of reconnection. Moving to 3D models, showing how fragmented current structures in kink-unstable twisted loops can both heat plasma and accelerate charged particles. Forward modelling of the observational signatures of this process in EUV, hard X-rays and microwaves will be described, and the potential for observational identification of twisted magnetic fields in the solar corona discussed. Then, coronal structure with multiple twisted threads will be considered, showing how instability in a single unstable twisted thread may trigger reconnection with stable neighbours, releasing their stored energy and causing an "avalanche" of heating events, with important implications for solar coronal heating. This avalanche can also accelerate electrons and ions throughout the structure. Many other stars exhibit flares, and I will briefly discuss recent work on modelling radio emission in flares in young stars (T Tauri stars). In particular, the enhanced radio luminosity of these stars relative to scaling laws for the Sun and other Main Sequence stars will be discussed.

Apr 5 Fri Luca Pol THH reading group

Apr 4 Thu Chris Birkbeck (UCL) Number Theory seminar
Following a construction of Chojecki-Hansen-Johansson, we use Scholze's infinite level modular varieties and the Hodge-Tate period map to give a new definition of overconvergent elliptic and Hilbert modular forms which is analogous to the standard construction of modular forms as functions on the upper half plane. This has applications to constructing overconvergent Eichler-Shimura maps in these settings. This is all work in progress joint with Ben Heuer and Chris Williams.

Apr 4 Thu Richard Hepworth (Aberdeen) Topology seminar

Apr 3 Wed Mahesh Kakde (King's College London) Pure Maths Colloquium
I will introduce the Gross-Stark units and present their application to Hilbert’s 12th problem. Following an earlier work in special case with Darmon, Dasgupta gave precise conjectural p-adic analytic formula for these units. After giving a formulation of this conjecture, I will sketch a proof of this conjecture. This is a joint work in progress with Samit Dasgupta.

Apr 3 Wed Matt Turner (Surrey) Applied Mathematics Colloquium
In this talk we examine two-dimensional, inviscid, irrotational fluid sloshing in both fixed and moving vessels. In particular we focus on a numerical scheme which utilizes time-dependent conformal mappings of doubly-connected domains to produce a scheme which is fast and efficient. Results are presented for flows in a fixed vessel, a moving vessel with bottom topography, a coupled pendulum slosh problem and a fixed vessel with multiple horizontal baffles. The application of this work is to the modelling of offshore wave energy converters.

Apr 2 Tue Matthew Allcock, Farhad Allian, Callum Reader (Sheffield) Postgraduate seminars
Matthew Allcock - The mathematics of making the right decisions
In philosophy, there are two types of uncertainty: empirical uncertainty - uncertainty about what “is” - and normative uncertainty - uncertainty about what “should be”. We know how to deal with empirical uncertainty - we use expected value theory. But how should we deal with normative uncertainty? It turns out that we can define a mathematical framework analogous to expected value theory that deals with normative uncertainty. This framework works… sometimes… until it breaks. Let’s try to fix those breaks using mathematics.

Farhad Allian - Observations of solar coronal loop oscillations
Imagine you're hiking up the highest hill in the Peak District. But to your disbelief, you notice that your surrounding air becomes hotter as you approach the summit. This is exactly what happens on our Sun: The solar atmosphere is around 200 times hotter than its surface, and this seemingly paradoxical statement has left solar physicists puzzled for decades. In this talk, I will present my research on how I'm combining high-resolution images with mathematics to understand how the Sun's atmosphere can be heated to 2,000,000 Kelvin.

Callum Reader - Biodiversity metrics from category theory
In 1973 philosopher and mathematician Lawvere published his paper “Metric Spaces, Generalised Logic, and Closed Categories”, outlining the theory of enriched categories: a generalisation common of both regular categories and metric spaces. Around forty years later, Leinster introduced the concept of magnitude (a generalisation of Euler characteristic) for an enriched category, distilling all its information to a single value in some ring. Interestingly, when specifically applied to a metric space this seems to give some information about the “effective number of points” of the space, providing a better means of measuring biodiversity and answering the age old question: “yeah but what are the applications?”

Apr 2 Tue Arne Grauer, Lukas Lüchtrath (Cologne) Statistics Seminar
We consider a class of growing graphs embedded into the $d$-dimensional torus where new vertices arrive according to a Poisson process in time, are randomly placed in space and connect to existing vertices with a probability depending on time, their spatial distance and their relative ages. This simple model for a scale-free network is called the age-based spatial preferential attachment network and is based on the idea of preferential attachment with spatially induced clustering. The graphs converge weakly locally to a variant of the random connection model, which we call the age-dependent random connection model. This is a natural infinite graph on a Poisson point process where points are marked by a uniformly distributed age and connected with a probability depending on their spatial distance and both ages. We use the limiting structure to investigate asymptotic degree distribution, clustering coefficients and typical edge lengths in the age-based spatial preferential attachment network.

Mar 29 Fri Jordan Williamson THH reading group

Mar 28 Thu Stanislav Gunár (Astronomical Institute of the Czech Academy of Sciences) SP2RC seminar
To understand the links between the distribution of the prominence plasma, the configuration of its magnetic field and the observations of prominence/filament fine structures obtained in UV/EUV, optical and radio domains from various vantage points, we need complex 3D prominence models. We have developed two such models which combine 3D magnetic field configurations of an entire prominence with a detailed description of the prominence plasma distributed along hundreds of fine structures. The first 3D Whole-Prominence Fine Structure (WPFS) model, developed by Gunár & Mackay (2015), uses a magnetic field configuration obtained from non-linear force-free field simulations of Mackay & van Ballegooijen (2009). The second WPFS model was developed by Gunár, Dudík, Aulanier, Schmieder & Heinzel (2018). The model employs a magnetic field configuration of a polar crown prominence based on the linear force-free field modelling approach designed by Aulanier & Démoulin (1998) which allows us to calculate linear magneto-hydrostatic extrapolations from photospheric flux distributions. The prominence plasma in both models is located in magnetic dips that occur naturally in the predominantly horizontal prominence magnetic field. This plasma has a realistic distribution of the density and temperature, including the prominence-corona transition region. The models thus provide comprehensive information about the 3D distribution of the prominence plasma and magnetic field which can be consistently studied both as a prominence on the limb and as a filament on the disk. These models can be visualized for example in the H-alpha spectral line. Together with the models, we will present some of their capabilities which allow us to study the evolution of prominences/filaments or to analyze the true and apparent shapes and motions of the prominence fine structures.

Mar 28 Thu Mark Quinn (Sheffield) Teaching Lunch

Mar 28 Thu Jeremy Oakley (Sheffield) Statistics Seminar
We will be spending two seminar slots on the following: Variational Inference: A Review for Statisticians David M. Blei, Alp Kucukelbir, Jon D. McAuliffe

Mar 28 Thu Jordan Williamson (Sheffield) Topology seminar
Greenlees-Shipley developed a Cellularization Principle for Quillen adjunctions in order to attack the problem of constructing algebraic models for rational G-spectra. One example of this was the classification of free rational G-spectra as torsion modules over the cohomology ring H*(BG) (for G connected). This has some disadvantages; namely that it is not monoidal and that torsion modules supports only an injective model structure. I will explain a related method called the Left Localization Principle, and how this can be used to construct a monoidal algebraic model for cofree G-spectra. This will require a tour through the different kinds of completions available in homotopy theory. This is joint work with Luca Pol.

Mar 27 Wed Daniele Avitabile (Nottingham) Applied Mathematics Colloquium
We will discuss level-set based approaches to study the existence and bifurcation structure of spatio-temporal patterns in biological neural networks. Using this framework, which extends previous ideas in the study of neural field models, we study the first example of canards in an infinite-dimensional dynamical system, and we give a novel characterisation of localised structures, informally called “bumps”, supported by spiking neural networks. We will initially consider a spatially-extended network with heterogeneous synaptic kernel. Interfacial methods allow for the explicit construction of a bifurcation equation for localised steady states. When the model is subject to slow variations in the control parameters, a new type of coherent structure emerges: the structure displays a spatially-localised pattern, undergoing a slow-fast modulation at the core. Using interfacial dynamics and geometric singular perturbation theory, we show that these patterns follow an invariant repelling slow manifold, hence we name them "spatio-temporal canards". We classify spatio-temporal canards and give conditions for the existence of folded-saddle and folded-node canards. We also find that these structures are robust to changes in the synaptic connectivity and firing rate. The theory correctly predicts the existence of spatio-temporal canards with octahedral symmetries in a neural field model posed on a spherical domain. We will then discuss how the insight gained with interfacial dynamics may be used to perform coarse-grained bifurcation analysis on neural networks, even in models where the network does not evolve according to an integro-differential equation. As an example I will consider a well-known event-driven network of spiking neurons, proposed by Laing and Chow. In this setting, we construct numerically travelling waves whose profiles possess an arbitrary number of spikes. An open question is the origin of the travelling waves, which have been conjectured to form via a destabilisation of a bump solution. We provide numerical evidence that this mechanism is not in place, by showing that disconnected branches of travelling waves with countably many spikes exist, and terminate at grazing points; the grazing points correspond to travelling waves with an increasing number of spikes, a well-defined width, and decreasing propagation speed. We interpret the so called “bumps” and “meandering bumps”, supported by this model as localised states of spatiotemporal chaos, whereby the dynamics visits a large number of unstable localised travelling wave solutions.

Mar 27 Wed Andreea Mocanu (Nottingham) ShEAF: postgraduate pure maths seminar
Jacobi forms arise naturally in number theory, for example as functions of lattices or as Fourier-Jacobi coefficients of other types of modular forms. They have applications in algebraic geometry, string theory and the theory of vertex operator algebras, among other areas. We are interested in establishing a precise connection between Jacobi forms of lattice index and elliptic modular forms, in other to transfer information from one side to the other. In this talk, we illustrate this connection via an example, namely that of Jacobi forms whose indices are the root lattices of type $D_n$.

Mar 22 Fri Steffen Gielen (Nottingham) Applied Mathematics Colloquium
In the standard picture of cosmology, the Universe began at the Big Bang; the Big Bang itself is a singularity where the laws of physics break down. A quantum theory of gravity should resolve this singularity and help in understanding the initial state of the Universe needed to account for present observations. I will present some progress towards this goal in the group field theory approach to quantum gravity, using the idea of a universe formed as a "condensate", i.e. a very homogeneous quantum configuration, from a large number of discrete building blocks of geometry. I will show how this setting produces new cosmological models without an initial singularity; demanding that such models be both theoretically self-consistent and potentially compatible with observation then gives new ways for constraining theories of quantum gravity.

Mar 22 Fri Nicola Bellumat THH reading group

Mar 21 Thu Theo Kypraios (Nottingham) Statistics Seminar
Healthcare-associated infections (HCAIs) remain a problem worldwide, and can cause severe illness and death. It is estimated that 5-10% of acute-care patients are affected by nosocomial infections in developed countries, with higher levels in developing countries.
Statistical modelling has played a significant role in increasing understanding of HCAI transmission dynamics. For instance, many studies have investigated the dynamics of MRSA transmission in hospitals, estimating transmission rates and the effectiveness of various infection control measures. However, uncertainty about the true routes of transmission remains and that is reflected on the uncertainty of parameters governing transmission. Until recently, the collection of whole genome sequence (WGS) data for bacterial organisms has been prohibitively complex and expensive. However, technological advances and falling costs mean that DNA sequencing is becoming feasible on a larger scale.
In this talk we first describe how to construct statistical models which incorporate WGS data with regular HCAIs surveillance data (admission/discharge dates etc) to describe the pathogen's transmission dynamics in a hospital ward. Then, we show how one can fit such models to data within a Bayesian framework accounting for unobserved colonisation times and imperfect screening sensitivity using efficient Markov Chain Monte Carlo algorithms. Finally, we illustrate the proposed methodology using MRSA surveillance data collected from a hospital in North-East Thailand.

Mar 21 Thu Tom Fisher (Cambridge) Number Theory seminar
I will describe joint work with Bhargava and Cremona, and with Ho and Park, on the probability that a randomly chosen genus one curve is soluble over the p-adics. A striking feature of this work is that we obtain exact answers in the form of explicit rational functions of p. I will also discuss what is expected to happen globally.

Mar 21 Thu Mike Prest (Manchester) Topology seminar
There is a construction of Freyd which associates, to any ring R, the free abelian category on R. That abelian category may be realised as the category of finitely presented functors on finitely presented R-modules. It has an alternative interpretation as the category of (model-theoretic) imaginaries for the category of R-modules. In fact, this extends to additive categories much more general than module categories, in particular to finitely accessible categories with products and to compactly generated triangulated categories. I will describe this and give some examples of its applications.

Mar 21 Thu Peter Keys (Queen's University (Belfast)) Plasma Dynamics Group
Small-scale magnetic fields, ubiquitous across the solar surface, manifest as intensity enhancements in intergranular lanes and, thus, often receive the moniker of magnetic bright point (MBP). MBPs are frequently studied as they are considered as a fundamental building block of magnetism in the solar atmosphere. The theory of convective collapse developed in the late 70’s and early 80’s is often used to explain how kilogauss fields form in MBPs. The dynamic nature of MBPs coupled with these kilogauss fields means that they are frequently posited as a source of wave phenomena in the solar atmosphere. Here, with high resolution observations of the quiet Sun with full Stokes spectropolarimetry, we investigate the magnetic properties of MBPs. By analysing the temporal evolution of various physical properties obtained from inversions, we show that kilogauss fields in MBPs can appear due to a variety of reasons, and is not limited to the process of convective collapse. Analysis of MURaM simulations confirms the processes we observe in our data. Also, magnetic field amplification happens on rapid timescales, which has significant implications for many wave studies.

Mar 20 Wed Sven Meinhardt (Sheffield) Pure Maths Colloquium
The idea of moduli spaces classifying structures in various fields of mathematics dates back to Riemann who tried to classify complex structures on a compact surface. It took another hundred years and many ingenious ideas of Grothendieck, Mumford and other mathematicians to write down a proper definition of moduli spaces and to construct nontrivial examples including Riemann‘s vague idea of a moduli space of complex structures on a surface. However, it became quite obvious that the concept of moduli spaces/stacks developed in the 60‘s and 70‘s is not sufficient to describe all moduli problems. Another 50 years and a fair amount of homotopy theory was needed to provide a definition of moduli spaces having all required properties. A large class of examples comes from (higher) representation theory. The aim of my talk is to provide a gentle introduction into these new concepts and thereby to show how nicely algebraic geometry, topology and representation theory interact with each other. If time permits, I will also sketch applications in Donaldson-Thomas theory.

Mar 20 Wed Gianmarco Brocchi (Birmingham) ShEAF: postgraduate pure maths seminar
This will be a blunt talk on sharp inequalities. Roughly speaking, these are inequalities which cannot be improved. In particular, I will introduce inequalities for the restriction of the Fourier transform, explaining why I got interested in them and how they are related to other inequalities in PDE, such as Strichartz estimates. These are a key tool in understanding the evolution of waves in dispersive PDE. If time allows, I will discuss a sharp Strichartz estimate for the fourth order Schrödinger equation from a joint work with Diogo Oliveira e Silva and René Quilodrán.

Mar 15 Fri Jonathan Potts (Sheffield) Teaching Lunch
We explain our use of MOLE exams in MAS222 and why it is a win-win tool for students and staff alike. The "win" for staff is particularly wonderful as it removes that most onerous task: exam marking. We'll start with a very brief presentation of how to set a MOLE exam up and how we've used them in MAS222. Then we'll open the floor to discussion about how they might be used more widely in SoMaS.

Mar 15 Fri Luca Pol THH reading group

Mar 14 Thu Luca Giovannelli (University of Rome Tor Vergata) SP2RC seminar
The ubiquitous presence of small magnetic elements in the Quiet Sun represents a prominent coupling between the photosphere and the upper layers of the Sun’s atmosphere. Small magnetic element tracking has been widely used to study the transport and diffusion of the magnetic field on the solar photosphere. From the analysis of the displacement spectrum of these tracers, it has been recently agreed that a regime of super-diffusivity dominates the solar surface. In this talk we will focus on the analysis of the bipolar magnetic pairs in the solar photosphere and their diffusion properties, using a 25-h dataset from the HINODE satellite. Interestingly, the displacement spectrum for bipolar couples behaves similarly to the case where all magnetic pairs are considered. We also measure, from the same dataset, the magnetic emergence rate of the bipolar magnetic pairs and we interpret them as the magnetic footpoints of emerging magnetic loops. The measured magnetic emergence rate is used to constrain a simplified model that mimics the advection on the solar surface and evolves the position of a great number of loops, taking into account emergence, reconnection and cancellation events. In particular we compute the energy released by the reconnection between different magnetic loops in the nano-flares energy range. Our model gives a quantitative estimate of the energy released by the reconfiguration of the magnetic loops in a quiet Sun area as a function of height in the solar atmosphere, from hundreds of Km above the photosphere up to the corona, suggesting that an efficiency of ~10% in the energy deposition might sustain the million degree corona.

Mar 14 Thu Jeremy Oakley (Sheffield) Statistics Seminar
We will be spending two seminar slots on the following: Variational Inference: A Review for Statisticians David M. Blei, Alp Kucukelbir, Jon D. McAuliffe

Mar 14 Thu Neil Strickland (Sheffield) Topology seminar
I will describe an extremely easy construction with formal group laws, and a slightly more subtle argument to show that it can be done in a coordinate-free way with formal groups. I will then describe connections with a range of other phenomena in stable homotopy theory, although I still have many more questions than answers about these. In particular, this should illuminate the relationship between the Lambda algebra and the Dyer-Lashof algebra at the prime 2, and possibly suggest better ways to think about related things at odd primes. The Morava K-theory of symmetric groups is well-understood if we quotient out by transfers, but somewhat mysterious if we do not pass to that quotient; there are some suggestions that dilation will again be a key ingredient in resolving this. The ring $MU_*(\Omega^2S^3)$ is another object for which we have quite a lot of information but it seems likely that important ideas are missing; dilation may also be relevant here.

Mar 13 Wed Fatemeh Mohammadi (Bristol) Pure Maths Colloquium
Theory of divisors on graphs is analogous to the classical theory for algebraic curves. The combinatorial language in this setting is "chip-firing game” which has been independently introduced in other fields. A divisor on a graph is simply a configuration of dollars (integer numbers) on its vertices. In each step of the chip-firing game we are allowed to select a vertex and then lend one dollar to each of its neighbors, or borrow one dollar from each of its neighbors. The goal of the chip-firing game is to get all the vertices out of debt. In this setting, there is a combinatorial analogue of the classical Riemann-Roch theorem. I will explain the mathematical structure arising from this process and how it sits in a more general framework of (graphical) hyperplane arrangements.

Mar 13 Wed Tobias Grafke (Warwick) Applied Mathematics Colloquium
In stochastic systems, extreme events are known to be described by "instantons", saddle point configurations of the action of the associated stochastic field theory. In this talk, I will present experimental evidence of a hydrodynamic instanton in a real world fluid system: A 270m wave channel experiment in Norway. The experiment attempts to model conditions on the ocean in order to observe so-called rogue waves, realisations of extreme ocean surface elevation out of relatively calm surroundings. These rogue waves are also observed in the ocean, where they are rare and hard to predict but pose significant danger to naval vessels. We show that the instanton approach, which is rigorously grounded in large deviation theory, offers a unified description of rogue waves in the water tank, covering the entire range of parameters for deep water waves in the ocean. In particular, this approach allows for a unified description of both the predominantly linear and the highly nonlinear regimes, and is able to explain the experimental data in the tank regardless of the strength of the nonlinearity.

Mar 13 Wed Karoline Van Gemst (Birmingham) ShEAF: postgraduate pure maths seminar
Enumerative geometers are interested in counting certain geometric objects given a set of conditions. One example of such a counting problem is how many degree d rational curves pass through 3d-1 generically placed given points in the projective plane. This particular problem proved extremely difficult using classical methods, even for low d. In the 1990s however, a revolution within this area took place, originating in the world of physics. This led to Kontsevich solving the counting problem by proving a recursive formula for calculating this number for any d. Kontsevich’s formula requires a single initial datum, the case of d=1, which translates to the fact that a single line passes through two given points in the plane. In this talk, I will present some of the crucial ingredients in setting up for and proving Kontsevich’s formula, and illustrate how it makes sense through a few examples. If time permits, I will also motivate how the formula can be viewed as expressing the associativity of the quantum product.

Mar 12 Tue Giovanni Marchetti Algebraic Geometry Learning Seminar
Talk 1: Ouverture.

Mar 8 Fri Hope Thackray, Jake Percival, Bryony Moody (Sheffield) Postgraduate seminars
Hope Thackray - How do we see inside the Sun?
Much like the waves known to exist above the solar surface, the Sun itself exhibits a widespread pulsation, mimicking the beating of a heart. Sound waves resonate inside the Sun, buffeting the surface, and causing light emitted to experience Doppler-shifting. The structures of these resonant cavities may then be deduced from observations of these shifts, allowing us to "see'' the Sun's interior. Here, one such method of deriving the Sun's sub-surface flows is described, in a technique known as Ring Diagram Analysis.

Jake Percival - RNG's: How computers handle randomness
When we want a “random” number in everyday life, such as when playing a board game, we rely on processes that aren't truly random, such as rolling a die. Perhaps more reliable would be to ask a computer to produce a random number for us. The code used to give these numbers is called a Random Number Generator (RNG) and like rolling a die, they aren't truly random! But if they aren't random, what is actually happening “under the hood”? In this talk we'll look at how RNG's work and how they can go wrong, including a fun example from the world of video games!

Bryony Moody - The hidden layer of statistics in archaeology
This talk will give a brief overview of Bayesian inference and the concepts of prior and posterior knowledge. Then I will discuss the various forms of prior knowledge available in archaeology, as well as the data that are used in conjunction with the prior knowledge to form a posterior. Finally I will conclude by discussing the priors I am focusing on for my PhD and what my plans are for modelling them.

Mar 7 Thu Christian Fonseca Mora (Costa Rica) Statistics Seminar
In this talk we will give an introduction to SPDEs in spaces of distributions. In the first part of the talk we consider a model of environmental pollution with Poisson deposits that will help to introduce the basic concepts for the study of SPDEs on infinite dimensional spaces. In the second part of the talk, we introduce a generalized form of SPDEs in spaces of distributions and explain conditions for the existence and uniqueness of its solutions. For this talk we will not assume any previous knowledge on SPDEs.

Mar 7 Thu Jean-Stefan Koskivirta (Tokyo) Number Theory seminar
We explain an application of the existence of generalized Hasse invariants to show ampleness of certain line bundles on flag spaces of Shimura varieties of Hodge type in positive characteristic. These methods generalize to other types of schemes which carry a universal G-zip. We deduce vanishing results for the cohomology of automorphic vector bundles. We compare them with similar results of Lan-Suh.

Mar 7 Thu Irakli Patchkoria (Aberdeen) Topology seminar
The real topological Hochschild and cyclic homology (THR, TCR) are invariants for rings with anti-involution which approximate the real algebraic K-theory. In this talk we will introduce these objects and report about recent computations. In particular we will dicuss components of THR and TCR and some recent and ongoing computations for finite fields. This is all joint with E. Dotto and K. Moi.

Mar 7 Thu Patrick Antolin (University of St Andrews) Plasma Dynamics Group
A large amount of recent simulations and analytical work indicate that standing transverse MHD waves in loops should easily lead to the generation of dynamic instabilities at their edges, and in particular of the Kelvin-Helmholtz kind. While a direct observation of these transverse wave-induced Kelvin-Helmholtz rolls (or TWIH rolls) is still lacking, the forward modelling of these simulations give us an indication of what to look for in next generation instrumentation, and which currently observed features could actually be the result of TWIKH rolls. In this talk I will go through some of these results, comparing observations with various instruments with simulations of coronal loops, prominences and spicules.

Mar 7 Thu David Robinson (Capital One) RSS Seminar Series
David will start his talk with a brief history of Statistics and Data Science at Capital One: how we got here, what's changed, and what the current expectations and challenges are in the era of "Big Data" and "Machine Learning". The main technical focus will then be on the use of "Gradient Boosting Machines", which over the last few years have emerged as the modelling method of choice for most classification problems within Financial Services. David will cover what they are, why they have become popular and how many of the practical considerations and pitfalls of traditional statistical techniques still very much apply. Example uses will focus on credit risk and affordability, looking at how we can ensure we make fair lending decisions when faced with unfair and biased data.

Mar 6 Wed Matt Aldridge / Sarah Penington / Helena Stage / Henning Sulzbach (Leeds / Bath / Manchester / Birmingham) Probability in the North East

Mar 6 Wed Gwyneth Stallard (Open University) Pure Maths Colloquium
Complex dynamics concerns the iteration of analytic functions of the complex plane. For each function, the plane is split into two sets: the Fatou set (where the behaviour of the iterates is stable under local variation) and the Julia set (where the behaviour is chaotic). The dynamical behaviour of the iterates inside the periodic components of the Fatou set was classified into four different types by the founders of the subject and this classification has played a key role in the development of the subject. One of the most dramatic breakthroughs was given by Sullivan in the 1980s when he proved that, for rational functions, all components of the Fatou set are eventually periodic and there are no so-called wandering domains. For transcendental functions, however, wandering domains can exist and the rich variety of possible behaviours that can occur is only just becoming apparent.

Mar 6 Wed Rachael Hardman (SoMaS) Applied Mathematics Colloquium
High frequency, or HF, coastal radars can provide continuous high resolution measurements of ocean surface currents, winds and waves. First derived in 1972, the expected radar signal when electromagnetic waves are scattered by the ocean surface can be modelled by the radar cross section, a nonlinear integral equation which enables us to predict the radar output for any ocean state. Methods for inverting the radar cross section - which ultimately permit us to measure ocean parameters from HF radar data - have been developed over the last few decades; however there are times when the measured data cannot be modelled by the mathematical equations and are therefore not suitable for inversion using the existing methods. Using a neural network, trained on simulated radar data, we have successfully inverted HF radar data not modelled by the radar cross section. In this talk, I will give an overview of how HF radar is used in ocean sensing before introducing neural networks. I will finish by presenting the results of a validation experiment, showing how a neural network can learn the complex inverse relationship between HF radar and the ocean surface.

Mar 6 Wed Paolo Dolce (Nottingham) ShEAF: postgraduate pure maths seminar
I will give an overview of a novel approach to the study of two dimensional algebraic and arithmetic geometry by means of adelic and idelic structures. Particular emphasis will be given to the case of arithmetic surfaces since the aim of the theory is to give a two dimensional version of Tate's thesis.

Mar 1 Fri Luca Pol THH reading group

Feb 28 Thu Björn Löptien (Max Planck Institute for Solar System Research )
The Wilson depression is the difference in geometric height of the layer of unit continuum optical depth between the sunspot umbra and the quiet Sun. Measuring the Wilson depression is important for understanding the geometry of sunspots. Current methods suffer from systematic effects or need to make assumptions on the geometry of the magnetic field. This leads to large systematic uncertainties of the derived Wilson depressions. Here we present a method for deriving the Wilson depression that only requires the information about the magnetic field that are accessible by spectropolarimetry and that does not rely on assumptions on the geometry of sunspots or on its magnetic field. Our method is based on minimizing the divergence of the magnetic field vector derived from spectropolarimetric observations. We focus on large spatial scales only in order to reduce the number of free parameters. We test the performance of our method using synthetic Hinode data derived from two sunspot simulations. We find that the maximum and the umbral averaged Wilson depression for both spots determined with our method typically lies within 100 km of the true value obtained from the simulations. In addition, we apply the method to spots from the Hinode sunspot database at MPS. The derived Wilson depressions (500-700 km) are consistent with results typically obtained from the Wilson effect. In our sample, larger spots with a stronger magnetic field exhibit a higher Wilson depression than smaller spots.

Feb 28 Thu Dan Graves and Sarah Whitehouse Teaching Lunch
Sarah will start by talking about various changes that have been made to MAS221 Analysis to address issues of poor student engagement and poor exam performance. This includes use of the AiM online test system for mid-term assessment. Dan will present examples of the type of AiM questions that have been used in MAS221 and in MAS220 Algebra, including proofs and multiple choice questions.

Feb 28 Thu Wil Ward (Sheffield) Statistics Seminar
The state space representation of a Gaussian process (GP) models the dynamics of an unknown (non-linear) function as a white-noise driven Itô differential equation. Representation in this form allows for the construction of joint models that mix known dynamics (e.g. population) with latent unknown input. Where these interactions are non-linear, or observed through non-Gaussian likelihoods, there is no exact solution and approximation techniques are required. This talk introduces an approach using black box variational inference to model surrogate samples and estimate the underlying parameters. The approximations are compared with full batch solutions and demonstrated to be indistinguishable in two-sample tests. Software and implementation challenges will also be addressed.

Feb 28 Thu Scott Balchin (Warwick) Topology seminar
Prismatic homotopy theory is the study of stable monoidal homotopy theories through their Balmer spectrum. In this talk, I will discuss how one can use localised p-complete data at each Balmer prime in an adelic fashion to reconstruct the homotopy theory in question. There are two such models, one is done by moving to categories of modules, which, for example, recovers the algebraic models for G-equivariant cohomology theories. The other, newer model, works purely at the categorical level and requires the theory of weighted homotopy limits. This is joint work with J.P.C Greenlees.

Feb 28 Thu Mark Wrigley (Chair IOP Yorkshire) Plasma Dynamics Group
The 1201 Alarm Project is the restoration, exhibition and sharing of materials recorded in 1969 of the Apollo moon landings from a domestic television. The talk will review the Apollo flight plan, the recording technologies of the day and the impact that it had on the speaker. The materials will form the basis for an exhibition celebrating the 50th anniversary of moon landings to be held at the National Science and Media Museum in Bradford, Yorkshire.

Feb 27 Wed Raven Waller (Nottingham) ShEAF: postgraduate pure maths seminar
The arithmetic, algebraic, and topological properties of local fields are intimately related. For higher dimensional local objects these relationships begin to break down, and this may cause considerable difficulty when studying them. The notion of a level structure allows us to work around some of these issues. We will discuss various applications of level structures, including the explicit study of representations of reductive groups over higher dimensional local fields, which is also related to the geometric Langlands program.

Feb 22 Fri James Cranch THH reading group

Feb 21 Thu Farrell Brumley (Paris 13) Pure Maths Colloquium
In what sense can automorphic forms or Galois representations be viewed as rational points on an algebraic variety? One way to explore this question is by counting arguments. The first result in this direction dates back to an early theorem of Drinfeld, which computes the number of 2-dimensional Galois representations of a function field in positive characteristic; the resulting expression is reminiscent of a Lefschetz fixed point theorem on a smooth algebraic variety over a finite field. More recently it was observed that in the number field setting there are formal similarities between the asymptotic counting problems for rational points on Fano varieties and for automorphic representations on reductive algebraic groups. Very little is known in the latter context. I’ll discuss joint work on this topic with Djordje Milicevic, in which we (mostly) solve the automorphic counting problem on the general linear group. Our results can be viewed as being analogous to the well-known result of Schanuel on the number of rational points of bounded height on projective spaces. If time permits, I may also present a short argument, using sphere packings in large dimensions, to give upper bounds on such automorphic counts.

Feb 21 Thu Sophia Wright (Warwick) Statistics Seminar
This talk explores the robustness of large Bayesian Networks when applied in decision support systems which have a pre-specified subset of target variables. We develop new methodology, underpinned by the total variation distance, to determine whether simplifications which are currently employed in the practical implementation of such graphical systems are theoretically valid. This same process can identify areas of the system which should be prioritised if elicitation is required. This versatile framework enables us to study the effects of misspecification within a Bayesian network (BN), and also extend the methodology to quantify temporal effects within Dynamic BNs. Unlike current robustness analyses, our new technology can be applied throughout the construction of the BN model; enabling us to create tailored, bespoke models. For illustrative purposes we shall explore the field of Food Security within the UK.

Feb 20 Wed Farrell Brumley (Paris 13) Northern Number Theory Seminar
I will present some results on the concentration properties of automorphic forms obtained through the theta correspondence. Among other things, the method relies on a distinction principle for these lifts, which detect their functorial origin via the non vanishing of orthogonal periods. The examples we treat are in higher rank, and shed light on a purity conjecture of Sarnak. This is joint work with Simon Marshall.

Feb 20 Wed Heather Harrington (Oxford) Applied Mathematics Colloquium
Many biological problems, such as tumor-induced angiogenesis (the growth of blood vessels to provide nutrients to a tumor), or signaling pathways involved in the dysfunction of cancer (sets of molecules that interact that turn genes on/off and ultimately determine whether a cell lives or dies), can be modeled using differential equations. There are many challenges with analyzing these types of mathematical models, for example, rate constants, often referred to as parameter values, are difficult to measure or estimate from available data. I will present mathematical methods we have developed to enable us to compare mathematical models with experimental data. Depending on the type of data available, and the type of model constructed, we have combined techniques from computational algebraic geometry and topology, with statistics, networks and optimization to compare and classify models without necessarily estimating parameters. Specifically, I will introduce our methods that use computational algebraic geometry (e.g., Gröbner bases) and computational algebraic topology (e.g., persistent homology). I will present applications of our methodology on datasets involving cancer. Time permitting, I will conclude with our current work for analyzing spatio-temporal datasets with multiple parameters using computational algebraic topology. Mathematically, this is studying a module over a multivariate polynomial ring, and finding discriminating and computable invariants.

Feb 20 Wed Andreea Mocanu (University of Nottingham) Northern Number Theory Seminar
I will give a brief introduction to Jacobi forms, including some examples and their relation to other types of modular forms. After that, I will discuss some of the ingredients that go into developing a theory of newforms for Jacobi forms of lattice index, namely Hecke operators, level raising operators and orthogonal groups of discriminant modules.

Feb 20 Wed Clark Barwick (Edinburgh) Topology seminar
Half a century ago, Barry Mazur and David Mumford suggested a remarkable dictionary between prime numbers and knots. I will explain how the story of exodromy permits one to make this dictionary precise, and I will describe some applications.

Feb 15 Fri Dan Graves THH reading group

Feb 14 Thu Carolina Robustini (Stockholm University)
We present high spatial resolution narrow-band images in three different chromospheric spectral lines, including Ca II K with the new CHROMospheric Imaging Spectrometer installed at the Swedish 1-m Solar Telescope. These observations feature a unipolar region enclosed in a supergranular cell, and located 68º off the disk-centre. The observed cell exhibits a radial arrangement of the fibrils which recalls of a chromospheric rosette. However, in this case, the convergence point of the fibrils is located at the very centre of the supergranular cell. Our study aims to show how the chromosphere appears in this peculiar region and retrieve its magnetic field and velocity distribution. In the centre of the cell, we measured a significant blue-shift in the Ca II K nominal line core associated to an intensity enhancement. We interpreted it as the product of a strong velocity gradient along the line of sight. In this talk, we will discuss the techniques employed to obtain magnetic field maps so close to the limb and suggest a possible configuration that takes into account also the measured velocity within the unipolar region.

Feb 14 Thu Eleanor Stillman (Sheffield)
This talk will outline the process of directly applying to become a (associate-principal) fellow of the HEA. The talk will help Ph.D. students to Professors understand what is required in the application and how to be successful. We may also discuss the value and implications of receiving professional recognition from the HEA.

Feb 14 Thu Andrey Lazarev (Lancaster) Topology seminar
I will explain how the category of discrete monoids models the homotopy category of connected spaces. This correspondence is based on derived localization of associative algebras and could be viewed as an algebraization result, somewhat similar to rational homotopy theory (although not as structured). Closely related to this circle of ideas is a generalization of Adams’s cobar construction to general nonsimply connected spaces due to recent works of Rivera-Zeinalian and Hess-Tonks. (joint with J. Chuang and J. Holstein)

Feb 14 Thu Will Hulme / Nick Monk / Rhoda Hawkins (Manchester / Sheffield / Sheffield) RSS Seminar Series
AIMS is an academic network that enables Africa’s talented students to become innovators who propel scientific, educational and economic self-sufficiency. The RSS Local Group are delighted to welcome Will Hulme (University of Manchester, taught at AIMS Cameroon), Prof Nick Monk (University of Sheffield, SOMAS, taught at AIMS Ghana) and Dr Rhoda Hawkins (University of Sheffield, Department of Physics and Astronomy, taught at AIMS South Africa, Senegal and Ghana) to present on their experiences on the AIMS project. Tutor/lecturer opportunities that may be of interest will be highlighted.

Feb 13 Wed Ana Caraiani (Imperial) Pure Maths Colloquium
In 1916, Ramanujan made a conjecture that can be stated in completely elementary terms: he predicted an upper bound on the coefficients of a power series obtained by expanding a certain infinite product. In this talk, I will discuss a more sophisticated interpretation of this conjecture, via the Fourier coefficients of a highly symmetric function known as a modular form. I will give a hint of the idea in Deligne’s proof of the conjecture in the 1970’s, who related it to the arithmetic geometry of smooth projective varieties over finite fields. Finally, I will discuss generalisations of this conjecture and some recent progress on these using the machinery of the Langlands program. The last part is based on joint work with Allen, Calegari, Gee, Helm, Le Hung, Newton, Scholze, Taylor, and Thorne.

Feb 7 Thu Jeremy Colman (Sheffield) Statistics Seminar
Devastating consequences can flow from the failure of certain structures, such as coastal flood defences, nuclear installations, and oil rigs. Their design needs to be robust under rare (p < 0.0001) extreme conditions, but how can the designers use data typically from only a few decades to predict the size of an event that might occur once in 10,000 years? Extreme Value Theory claims to provide a sound basis for such far-out-of-sample prediction, and using Bayesian methods a full posterior distribution can be obtained. If the past data are supplemented by priors that take into account expert opinion, seemingly tight estimates result. Are such claims justified? Has all uncertainty been taken into account? My research is addressing these questions.

Feb 7 Thu Masahiro Nakahara (Manchester) Number Theory seminar
Let X be a smooth projective variety over a number field with a fibration into varieties that satisfy a certain condition. We study the classes in the Brauer group of X that never obstruct the Hasse principle for X. We prove that if the generic fiber has a zero-cycle of degree d over the generic point, then the Brauer classes whose orders are prime to d do not play a role in the Brauer-Manin obstruction. As a result we show that the odd torsion Brauer classes never obstruct the Hasse principle for del Pezzo surfaces of degree 2, certain K3 surfaces, and Kummer varieties.

Feb 6 Wed Viveka Erlandsson (Bristol) Pure Maths Colloquium
Consider a billiard table shaped as a Euclidean polygon with labeled sides. A ball moving around on the table determines a bi-infinite “bounce sequence” by recording the labels of the sides it bounces off. We call the set of all possible bounce sequences the “bounce spectrum” of the table. In this talk I will explain why the bounce spectrum essentially determines the shape of the table: with the exception of a very small family (right-angled tables), if two tables have the same bounce spectrum, then they have to be related by a Euclidean similarity. The main ingredient in proving this fact is a technical result about non-singular geodesics on surfaces equipped with flat cone metrics. This is joint work with Moon Duchin, Chris Leininger, and Chandrika Sadanand.

Jan 31 Thu Prof. Valery Nakariakov (Centre for Fusion, Space and Astrophysics, University of Warwick) Plasma Dynamics Group
Fast and slow magnetoacoustic waves are a promising tool for the seismological diagnostics of physical parameters of various plasma structures in the corona of the Sun. In particular, compressive waves can provide us with information about the thermodynamic equilibrium in the coronal plasma, and hence the heating function. Compressive perturbations of the thermodynamic equilibrium by magnetoacoustic waves can cause the misbalance of the radiative cooling and unspecified heating. The effect of the misbalance is determined by the derivatives of the combined heating/cooling function with respect to the plasma density and temperature, and can lead to either enhanced damping of the compressive oscillations or their magnification. Moreover, in the regime of strong misbalance, compressive MHD waves are subject to wave dispersion that can slow down the formation of shocks and can cause the formation of quasi-periodic wave trains.

Jan 25 Fri Kalevi Mursula (University of Oulu) SP2RC seminar

Jan 23 Wed Richard Webb (Cambridge) Pure Maths Colloquium
The braid groups were defined by Artin in 1925, and are usually defined in terms of strings in 3-dimensional space. However there is a fruitful 2-dimensional perspective of the braid groups as homeomorphisms (up to some natural equivalence) of a disc with holes, in other words, the braid groups are special cases of mapping class groups of surfaces. Mapping class groups can be viewed in a number of ways, and are of interest in several different fields, such as dynamics, algebraic geometry, surface bundles, hyperbolic geometry, to name a few. A key theorem that demonstrates this intradisciplinary feature is the Nielsen--Thurston classification. I will explain what the Nielsen--Thurston classification is, describe some basic examples and analogies, and highlight its importance. I will then explain how to view this from the geometric group theory perspective, and discuss my work with Mark Bell that uses this point of view to solve the conjugacy problem for mapping class groups in polynomial time. At the end of the talk I will discuss some new ideas that may lead to applications in knot theory via the braid groups.

Jan 18 Fri Norbert Gyenge (Sheffield) SP2RC seminar
This thesis investigates new approaches for predicting the occurrence of solar eruptive events based on coronal mass ejection (CME), solar flare and sunspot group observations. The scope of the present work is to study the spatio-temporal properties of the above-mentioned solar features. The analysis may also provide a deeper understanding of the subject of solar magnetic field reorganisation. Furthermore, the applied approaches may open opportunities for connecting these local phenomena with the global physical processes that generate the magnetic field of the Sun, called the solar dynamo. The investigation utilises large solar flare statistical populations and advanced computational tools, such as clustering techniques, wavelet analysis, autoregressive moving average (ARIMA) forecast, kernel density estimations (KDEs) and so on. This work does not attempt to make actual predictions because it is out of the scope of the recent investigation. However, the thesis introduces new possible approaches in the subject of flare and CME forecasting. The future aim is to construct a real-time database with the ability to forecast eruptive events based on the findings of this thesis. This potential forecasting model may be crucial for protecting a wide range of satellite systems around the Earth or predicting space weather based on the obtained results may also assist to plan safe space exploration in the future.

Jan 17 Thu Ricardo Gaferia (Instituto de Astrofísica de Andalucía - CSIC ) SP2RC seminar
With the increase of data volume and the need of more complex inversion codes to interpret and analyze solar observations, it is necessary to develop new tools to boost inversions and reduce computation times and costs. In this presentation, I discuss the possibilities and limitations of using machine learning as a tool to estimate optimum initial physical atmospheric models necessary for initializing spectral line inversions. Tests have been carried out for the SIR and DeSIRer inversion codes. This approach allows firstly to reduce the number of cycles in the inversion and increase the number of nodes and secondly to automatically cluster pixels which is an important step to invert maps where completely different regimes are present. Finally, I also present a warp for SIR and DeSIRer inversion codes that allows the user to easily set up parallel inversions.

Jan 16 Wed Atsushi Takahashi (Osaka) Algebra / Algebraic Geometry seminar
In ’77 Orlik-Randell asked about the existence of a certain distinguished basis of vanishing cycles in the Milnor fiber associated to an invertible polynomial of chain type. With my student, Daisuke Aramaki we transport their conjecture to the category of matrix factorizations by the (conjectural) homological mirror symmetry equivalence and then prove the resulting statement.

Jan 8 Tue Josep Alvarez-Montaner (Universitat Politecnica de Catalunya) Algebra / Algebraic Geometry seminar
The aim of this talk is to give a detailed study of local cohomology modules of binomial edge ideals. Our main result is a Hochster type decomposition formula for these modules. As a consequence, we obtain a simple criterion for the Cohen-Macaulayness of these ideals and we describe their Castelnuovo-Mumford regularity and their Hilbert series. We also prove a conjecture of Conca, De Negri and Gorla relating the graded components of the local cohomology modules of binomial edge ideals and their generic initial ideals.