Seminars this semester


   Series:


Sep 19 Tue Elizabeth Winstanley (Sheffield) Cosmology, Relativity and Gravitation
15:00 J11, Hicks Quantum field theory on anti-de Sitter space-time
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Sep 21 Thu Sam Dolan (Sheffield) Cosmology, Relativity and Gravitation
14:00 J11, Hicks Geometrical optics and spin-helicity effects.
 
  Abstract:
The Belem group have recently shown a "spin-helicity effect" in the absorption of circularly-polarized electromagnetic & gravitational waves by a Kerr black hole, in which the counter-rotating helicity is more absorbed than the co-rotating helicity. The difference in the absorption cross sections scales with the inverse wavelength, so the helicity-dependence disappears in the zero-wavelength limit. The aim of this talk is to extend geometricaloptics beyond leading order to understand this effect.
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Sep 21 Thu Christopher Fewster (University of York) Cosmology, Relativity and Gravitation
15:00 J11, Hicks Preferred states in quantum field theories, ancient and modern
 
  Abstract:
The vacuum state of Minkowski space quantum field theory is distinguished as a state of maximal symmetry. General curved spacetimes have no nontrivial symmetry and therefore lack an obvious candidate vacuum state. Nonetheless, one might wonder whether there is still a way of selecting a preferred state and there have been many attempts in that direction. I will discuss various aspects of this issue, describing a general model-independent no-go theorem that excludes the existence of a local and covariant choice of preferred state. I will also discuss recently-introduced class of "SJ states" and its extensions.
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Sep 27 Wed Matthew Allcock/Mihai Barbulescu (Sheffield) Applied Mathematics Colloquium
14:00 Hicks, LT 9 Magneto-acoustic waves in asymmetric solar waveguides: magneto-seismology and the Kelvin-Helmholtz instability
 
  Abstract:
Matthew Allcock's abstract - Our Sun is a restless plasma with a strong and evolving magnetic field, making magnetohydrodynamics (MHD) an essential tool to describe its behaviour. The Sun’s atmosphere, where magnetic forces dominate, is permeated by MHD waves that can be used as an indirect method for diagnosing difficult-to-measure parameters of the solar plasma. This technique is known as solar magneto-seismology. In this talk, we will introduce a novel equilibrium structure consisting of two parallel discontinuities with a uniform magnetic field in the central region. We perturb the system and illustrate the eigenmodes using 3D animations to demonstrate the change in character of symmetric MHD wave modes when the system is asymmetric. We derive two methods that use this asymmetry to estimate the strength of the background magnetic field. This advances the field of solar magneto-seismology in locally asymmetric structures in the solar atmosphere.

Mihai Barbulescu's abstract - Solar plasma is highly dynamic and subject to various kinetic and magnetic forces. Many of these forces create bulk flows which need to be included in analytical models, especially when studying time dependent phenomena. Building up from the previous talk, we study the effects that a steady flow has on wave propagation in an asymmetric waveguide, and on its stability. When flow speeds are high enough, they force perturbations of the waveguide to steepen, and the Kelvin-Helmholtz instability (KHI) occurs. We calculate the critical values required by the KHI under different parameter regimes and discuss how these results may change how we view various solar phenomena.
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Sep 28 Thu Steven Julious and Jo Rothwell (Sheffield) RSS Seminar Series
16:00 Hicks LT2 Quantifying Effect Sizes in Clinical Trials
 
  Abstract:
Central to the validity of a RCT is a calculation of the number of participants required (the sample size) which provides reassurance that the trial will be informative. Conventionally, this is usually based upon a difference in the primary outcome (target difference) between groups that is desired to be detectable; the corresponding number of participants needed to be recruited is then calculated. From both a scientific and ethical standpoint, selecting an appropriate target difference is very important. However it has been neglected until relatively recently. A variety of approaches have been proposed and addressed by a large recent review. However there is need for greater guidance to aid researchers and funders. The DELTA2 study was commissioned by two UK academic trial funders (MRC and NIHR) to improve guidance in this area. However the project has engaged stakeholders from all sectors and the recommendations applicable to all clinical trials whether they be academic or industry sponsored. This session will present findings from this project and related work as part of a process of engagement with stakeholders prior to finalizing the guidance on specifying the target difference in a randomized trial sample size calculation.
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Oct 2 Mon Etienne Farcot (Nottingham) Mathematical Biology Seminar Series
14:00 Alfred Denny Conference Room Examples of Boolean modelling in plant development
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Oct 3 Tue Beth Romano (Cambridge) Number Theory seminar
13:00 J11 On the arithmetic of simple singularities of type E
 
  Abstract:
Given a simply laced Dynkin diagram, one can use Vinberg theory of graded Lie algebras to construct a family of algebraic curves. In the case when the diagram is of type $E_7$ or $E_8$, Jack Thorne and I have used the relationship between these families of curves and their associated Vinberg representations to gain information about integral points on the curves. In my talk, I’ll focus on the role Lie theory plays in the construction of the curves and in our proofs.
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Oct 3 Tue Dave Applebaum (TUOS)
15:00 Hicks, LT 6 Introduction to reproducing kernel Hilbert spaces
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Oct 4 Wed Chris Nelson (University of Sheffield) SP2RC Discussion & Book Group
13:00 Hicks LT10 An introduction to data analysis using SDO
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Oct 4 Wed Anna Felikson (University of Durham) Pure Maths Colloquium
14:00 J11 Quiver mutations, reflection groups and curves on punctured disc
 
  Abstract:

Mutations of quivers were introduced by Fomin and Zelevinsky in 2002 in the context of cluster algebras. For some classes of quivers, mutations can be realised using geometric or combinatorial models. We will discuss a construction of a geometric model for all acyclic quivers. The construction is based on the geometry of reflection groups acting in quadratic spaces. As an application, we show an easy and explicit way to characterise real Schur roots (i.e. dimension vectors of indecomposable rigid representations of Q over the path algebra kQ), which proves a recent conjecture of K.-H. Lee and K. Lee for a large class of acyclic quivers.

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Oct 4 Wed Zijing Ding (Bristol) Applied Mathematics Colloquium
14:00 Hicks, LT 9 Thin liquid film flowing down a vertical fibre
 
  Abstract:
We consider the motion of a gravity-driven flow coating a vertical fibre rotating about its axis. This flow exhibits rich dynamics including the formation of droplets, or beads, driven by a Rayleigh-Plateau mechanism modified by the presence of gravity and rotation. We derived an evolution equation for the film thickness using a long-wave approximation. We focus on the effect of rotation on the linear stability, absolute-convective instabilities (CI/AI), nonlinear evolution and the travelling solutions. The results of the linear stability analysis show that the effect of rotating is destabilizing. A spatial-temporal stability analysis is performed to investigate the convective-absolute instability characteristics of the problem. We also perform a numerical simulation on the nonlinear evolution of the film to examine the transition from CI to AI regime. It has been shown that the effect of rotation enhances the absolute instability and promotes the breakup of the film into smaller droplets. The travelling wave solutions of the evolution equation yield information regarding the shape of the interface and propagation speed of the disturbance
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Oct 4 Wed Eoin Murphy ShEAF: postgraduate pure maths seminar
16:00 Hicks Room J11 t = 1 Limits of Hall Algebras and Quantum Groups
 
  Abstract:
In this talk I hope to discuss how two isomorphic algebras degenerate on setting a parameter t=1. One of these is the quantum group Q associated to a simple Lie algebra. The other is a Hall algebra H of a certain category of complexes of quiver representations. The interesting thing is that for either algebra there are in fact different "ways to set t=1" resulting in different degenerate algebras. On the one hand one gets the universal enveloping algebra of a Lie algebra, on the other a Poisson algebra of functions on a Poisson-Lie group. We describe the t=1 theory of H and explain how it is related to that of Q. The story involves work for my PhD thesis and builds on results due to Ringel, Bridgeland, Deng, Chen and others.
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Oct 5 Thu Simon Willerton (Sheffield) Topology seminar
16:00 J11 The magnitude of odd balls
 
  Abstract:
Tom Leinster introduced the magnitude of finite metric spaces by formal analogy with his notion of Euler characteristic of finite categories. This can be thought of an 'effective number of points' n the metric space. It soon became clear that this notion of magnitude could
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Oct 6 Fri Neil Strickland Chromatic homotopy theory reading seminar
13:00 J11 An introduction to chromatic homotopy theory
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Oct 10 Tue Daniel Loughran (Manchester) Number Theory seminar
13:00 J11 Determinants as sums of two squares
 
  Abstract:
A classical theorem due independently to Landau and Ramanujan gives an asymptotic formula for the number of integers which can be written as a sum of two squares. We prove an analogous result for the determinant of a matrix using the spectral theory of automorphic forms. This is a special case of a more general result on a problem of Serre concerning specialisations of Brauer group elements on semisimple algebraic groups. This is joint work with Sho Tanimoto and Ramin Takloo-Bighash.
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Oct 10 Tue Antonin Coutant (Nottingham) Cosmology, Relativity and Gravitation
16:00 J11, Hicks The draining bathtub experiment
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Oct 11 Wed Susan Sierra (University of Edinburgh) Pure Maths Colloquium
14:00 J11 Noncommutative birational geometry
 
  Abstract:

One of the motivating problems in ring theory in the past twenty-five years has been the classification of noncommutative projective surfaces: that is, classifying all noetherian N-graded rings of cubic growth. In particular, one may ask: Fix a division ring D. What are the N-graded rings as above that are contained in the polynomial extension D[t] and have the same (graded) division ring of fractions? This is known as "classifying noncommutative surfaces birational to D''.

This question is particularly interesting where D is the division ring which comes from the famous Sklyanin algebra: a graded ring which behaves like the coordinate ring of a noncommutative version of the projective plane. Remarkably, although this situation is highly noncommutative, many of the famous theorems of (commutative) algebraic geometry of surfaces have very strong analogues. We describe how to do birational geometry in this noncommutative context, including noncommutative versions of blowing up a point and contracting a curve. However, these techniques, when applied to noncommutative rings, have applications which are extremely counterintuitive when compared with the commutative context.

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Oct 11 Wed Ed Ryan (Lancaster) Uncertainty Quantification study group
14:00 Hicks LT A Calibrating a global atmospheric chemistry transport model using a Gaussian process emulator and measurements of surface ozone and surface CO
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Oct 11 Wed Jordan Williamson (Sheffield) ShEAF: postgraduate pure maths seminar
16:00 J11 Hicks Morita Theory in Stable Homotopy Theory
 
  Abstract:
Morita theory was developed in the 1950s as a tool for studying rings by studying their categories of modules. Since then, reincarnations of Morita theory for abelian categories, derived categories and stable model categories have been developed. We will outline the classical version of Morita theory, the extension to the world of stable homotopy theory, and then use this extension to show how this result can be powerful in the search for algebraic models of spectra.
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Oct 12 Thu Dino Sejdinovic (Oxford) Statistics Seminar
14:00 LT 9 Approximate Kernel Embeddings and Symmetric Noise Invariance
 
  Abstract:
Kernel embeddings of distributions and the Maximum Mean Discrepancy (MMD), the resulting distance between distributions, are useful tools for fully nonparametric hypothesis testing and for learning on distributional inputs. I will give an overview of this framework and present some of the applications of the approximate kernel embeddings to Bayesian computation. Further, I will discuss a recent modification of MMD which aims to encode invariance to additive symmetric noise and leads to learning on distributions robust to the distributional covariate shift, e.g. where measurement noise on the training data differs from that on the testing data. https://arxiv.org/abs/1703.07596
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Oct 12 Thu Akos Matszangosz Topology seminar
16:00 J11 Real enumerative geometry and equivariant cohomology: Borel-Haefliger type theorems
 
  Abstract:
Enumerative geometry studies questions of the type: how many geometric objects satisfy a prescribed set of (generic) conditions? Over the complex field the answer is a single number. However, over R the answer depends on the configuration. A theorem of Borel and Haefliger states that mod 2 the answer is the same. Thom realized, that for a generic a) smooth, b) holomorphic map f, the cohomology class [Si(f)] of the singular points of f of a given type can be expressed as a universal polynomial evaluated at the characteristic classes of the map. The second theorem of Borel and Haefliger states that mod 2, the universal polynomial is the same in the smooth and holomorphic case. In this talk I plan to discuss these questions from the point of view of equivariant topology. The spaces satisfying the condition of the Borel-Haefliger theorem are part of a class of Z2-spaces called conjugation spaces introduced by Hausmann, Holm and Puppe. Analogously we introduce a class of U(1)-spaces which we call circle spaces in an attempt to say something more than parity about these questions. This is joint work with László Fehér.
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Oct 13 Fri Dr Jiajia Liu (University of Sheffield) SP2RC seminar
13:00 LT 11 Solar jets
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Oct 13 Fri Daniel Graves Chromatic homotopy theory reading seminar
14:00 J11 Formal group laws and Lazard's theorem
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Oct 17 Tue Lassina Dembele (King's College London) Number Theory seminar
13:00 J11 On the compatibility between base change and Hecke action
 
  Abstract:
Let $F/E$ be a Galois extension of totally real number fields. In this talk, we will discuss the action of $Gal(F/E)$ on Hecke orbits of automorphic forms on $GL_2$. This reveals some compatibility between base change and Hecke action, which has several implications for Langlands functoriality.
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Oct 17 Tue Alexander Vishik (Nottingham) Algebra / Algebraic Geometry seminar
14:00 J11 Subtle Stiefel-Whitney classes
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Oct 17 Tue Andrew Morozov (Leicester) Mathematical Biology Seminar Series
15:00 Hicks LT 10 Revisiting the concept of evolutionary fitness in systems with inheritance.
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Oct 18 Wed Hovhannes Khudaverdian (University of Manchester) Pure Maths Colloquium
14:00 J11 Thick morphisms and Koszul brackets
 
  Abstract:

We show an application of the new notion of a thick morphism of (super)manifolds.

For an arbitrary manifold $M$, consider the supermanifolds $\Pi TM$ and $\Pi T^*M$, where $\Pi$ is the parity reversion functor. The space $\Pi TM$ has an odd vector field that can be identified with the canonical de Rham differential $d$; functions on it can be identified with differential forms on $M$. The space $\Pi T^*M$ has an odd Poisson bracket $[ - , - ]$; functions on it can be identified with multivector fields on $M$ and the bracket is the canonical Schouten bracket. An arbitrary even function $P$ which obeys the master-equation $[P,P]=0$ defines an even homotopy Poisson structure on the manifold $M$ and an odd homotopy Poisson structure (the "higher Koszul brackets") on differential forms on $M$.

In the case when the function $P$ is quadratic on fibres, then the homotopy Poisson structure on $M$ and the higher Koszul bracket on differential forms are ordinary even and odd Poisson structures. It is a classical fact that there is a linear map of differential forms endowed with the Koszul bracket to multivector fields endowed with the canonical odd Schouten bracket $[ -, - ]$. In the general case, when we have a homotopy Poisson structure on $M$, this linear map does not exist. We show how to construct a non-linear transformation from differential forms endowed with the higher Koszul brackets to multivector fields with the canonical Schouten bracket. This is done as a non-linear pullback with respect to some thick morphism of supermanifolds, a notion recently introduced.

(The talk is based on the work with Ted Voronov.)

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Oct 18 Wed Thomas Prince (Imperial) Algebra / Algebraic Geometry seminar
15:00 J11 From period integrals to toric degenerations of Fano manifolds
 
  Abstract:
Given a Fano manifold we will consider two ways of attaching a (usually infinite) collection of polytopes, and a certain combinatorial transformation relating them, to it. The first is via Mirror Symmetry, following a proposal of Coates-Corti-Kasprzyk-Galkin-Golyshev. The second is via symplectic topology, and comes from considering degenerating Lagrangian torus fibrations. We then relate these two collections using the Gross--Siebert program. I will also comment on the situation in higher dimensions, noting particularly that by 'inverting' the second method (degenerating Lagrangian fibrations) we can produce topological constructions of Fano threefolds.
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Oct 18 Wed Angelo Rendina (Sheffield) ShEAF: postgraduate pure maths seminar
16:00 J11 Hicks Ramanujan sums, the Casimir effect and the Riemann zeta function
 
  Abstract:
In 1913 Ramanujan claimed in a letter to Hardy that $1+2+3+4+...=-1/12$, proving it with elementary methods. We also find examples of such divergent series appearing in some quantum physics phenomena, e.g. the Casimir effect, where a suitable renormalization allows to deal with converge problems; again, we find the same value of $-1/12$. The theory of analytic functions and meromorphic continuation makes sense of this absurd value: in particular, we will see how to extend the generalized harmonic series to the whole complex plane and find its functional equation.
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Oct 19 Thu Mauricio Alvarez (Sheffield) Statistics Seminar
14:00
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Oct 19 Thu Xue-Mei Li (Imperial) Probability
14:00 LT3 Brownian motions, Brownian Bridges and all that…
 
  Abstract:
BMs are well understood, Brownian bridges are conditioned Brownian motions and are well understood as such. On an Euclidean space, each induces a Gaussian measures on the space of paths. They are the Wiener measures. These measures can be used to construct Dirichlet forms and Ornstein-Uhlenbeck processes. Brownian bridges play the role of a delta measure and can be used for heat kernel estimates. In this talk we explore Brownian bridges, semi-classical bridges and even `generalized Brownian bridges’ for general elliptic differential operators.
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Oct 20 Fri Hope Thackray (Sheffield) SP2RC seminar
13:00 LT11 Ring Diagram Analysis
 
  Abstract:
In helioseismology, acoustic waves within the Sun are studied in order to derive sub-surface properties. One such helioseismological technique is known as Ring Diagram Analysis, first described in Hill (1988). Spectral data of Doppler shifted flows at the surface of the Sun can be used to deduce flow estimates beneath. Here, I illustrate the analysis using Global Oscillation Network Group (GONG) data.
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Oct 20 Fri Igor Sikora Chromatic homotopy theory reading seminar
14:00 J11 Complex oriented cohomology theories
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Oct 24 Tue Henri Johnston (Exeter) Number Theory seminar
13:00 J11 The p-adic Stark conjecture at s=1 and applications
 
  Abstract:
Let E/F be a finite Galois extension of totally real number fields and let p be a prime. The `p-adic Stark conjecture at s=1' relates the leading terms at s=1 of p-adic Artin L-functions to those of the complex Artin L-functions attached to E/F. When E=F this is equivalent to Leopoldt’s conjecture for E at p and the ‘p-adic class number formula’ of Colmez. In this talk we discuss the p-adic Stark conjecture at s=1 and applications to certain cases of the equivariant Tamagawa number conjecture (ETNC). This is joint work with Andreas Nickel.
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Oct 24 Tue Pierrick Bousseau (Imperial) Algebra / Algebraic Geometry seminar
14:00 J11 Quantum mirrors of log Calabi-Yau surfaces
 
  Abstract:
I will start describing the Gross-Hacking-Keel realization of mirror symmetry for log Calabi-Yau surfaces: the mirror variety is constructed by gluing elementary pieces together according to some gluing functions determined by counting rational curves in the original variety. I will then explain how to construct non-commutative deformations of these mirrors by including contributions of counts of higher genus curves in the original variety.
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Oct 25 Wed Ivan Cheltsov (University of Edinburgh) Pure Maths Colloquium
14:00 J11 Finite collineation groups and birational geometry
 
  Abstract:
Finite groups acting linearly on complex projective spaces have been studies by many people including Blichfeldt, Brauer, Lindsey, Wales, Collins, Thompson and Robinson. In dimension one (projective line) they had been classified in antiquity. Aside from cyclic and dyhedral groups, there are just three such groups, which are the groups of symmetries of Platonic solids. In higher dimensions, the classification is much more complicated. Finite subgroups of the projective transformations of the plane have been classified by Blichfeldt in 1917. He also classified finite subgroups of projective transformations of the three-dimensional space. In my talk I will describe Blichfeldt's classification and explain how to use it to describe equivariant birational geometry of the projective plane and three-dimensional space.
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Oct 25 Wed James Mather (Sheffield) Applied Mathematics Colloquium
14:00 Hicks, LT 9 Flow Instabilities in Partially Ionised Plasmas: Dissipative and Resonant Instabilities
 
  Abstract:
The solar atmosphere is a vastly complex and dynamic area, containing many different magnetic structures. The temperature can vary from approximately 4500 K at the temperature minimum to over 10 MK in parts of the solar corona. This temperature stratification affects how ionised the solar plasma is at different layers. Prominences are largely characterised as chromospheric material, at approximately 10000 K, suspended within the coronal plasma and, therefore, may not be fully ionised. They are also very dynamic and may exhibit bulk flows, with observations showing the presence of numerous instabilities. In this talk we firstly briefly introduce the fully ionised magnetic plasma slab moving under. Next, we investigate a plasma slab that has a uniform background bulk flow in the single fluid approximation, where partial ionisation is considered in Cowling’s resistive term in the induction equation, modelling a prominence surrounded by a viscous corona. We study the dissipative instability that can occur at flow speeds that match the internal tube/slow speed. Secondly, we set up a completely two fluid magnetic slab (ions and neutrals) moving under a bulk flow and investigate, in both the compressible and incompressible cases, a quasi-resonant instability that occurs between a new mode, that appears due to neutral molecules, which is always KHI unstable for any shear in flow and the normal magneto-acoustic modes of a slab moving under a uniform bulk flow.
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Oct 25 Wed Giovanni Marchetti (Sheffield) ShEAF: postgraduate pure maths seminar
16:00 J11 Hicks Perverse dimensions
 
  Abstract:
Exactly 100 years ago, Felix Hausdorff came up with the original idea that some geometrical objects might have non-integer dimension. However, very few steps have been made in homological algebra to pursue this idea. We discuss how the formalism of Bridgeland's stability can be exploited to build homology objects indexed by sets more general than the integers. Finally, we borrow an example from the theory of perverse sheaves to show that dimensions could be even worse behaved: they could be uncomparable.
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Oct 26 Thu Sam Cohen (Oxford) Probability
14:00 LT 3 Statistical Uncertainty and nonlinear expectations
 
  Abstract:
In stochastic decision problems, one often wants to estimate the underlying probability measure statistically, and then to use this estimate as a basis for decisions. We shall consider how the uncertainty in this estimation can be explicitly and consistently incorporated in the valuation of decisions, using the theory of nonlinear expectations.
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Oct 26 Thu Scott Balchin (Sheffield) Topology seminar
16:00 J11 Lifting cyclic model structures to the category of groupoids
 
  Abstract:
Abstract: We consider the problem of lifting certain Quillen model structures on the category of cyclic sets to the category of groupoids, echoing the construction of the Thomason model structure on Cat. We prove that this model structure only captures the theory of homotopy 1-types, and as a consequence, that SO(2)-equivariant homotopy 1-types cannot be encoded in a discrete manner. We will fully describe all of the components required for this model structure, in particular, assuming no familiarity with the model structures on cyclic sets or the Thomason model structure on Cat. This work is joint with Richard Garner.
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Oct 27 Fri Yudong Ye (National Space Science, Beijing) SP2RC seminar
13:00 LT 11 A Brief Introduction of Machine Learning and its Application in Space Physics
 
  Abstract:
Machine learning is more and more useful in this data explosion era and could be a powerful tool to reveal hidden connections and pave the way to new discoveries. In this talk, I will give an introduction to machine learning covering from its concepts, brief history, and different categories to its recent applications in space physics. With an example of deciding whether there is a strong geomagnetic storm (namely, the Dst index is less than -100) from ICME’s plasma and magnetic field parameters using support vector machine, I’ll explain step by step on how to apply machine learning method on a specific problem.
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Oct 27 Fri Akos Matszangosz Chromatic homotopy theory reading seminar
13:00 J11 Complex bordism - Part 1
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Oct 27 Fri Mathias Fuchs (Zaha Hadid Architects) Non-commutative Geometry, Analysis and Groups
14:45 J-11 Operator K-theory, Lie groups and lattices
 
  Abstract:
We will give a short glimpse into $K$-theory of $C^*$-algebras associated with Lie groups of low real rank, and with their discrete subgroups. We will subsequently report on work which computes the $K$-theory of the reduced group $C^*$-algebra of the Bianchi groups, making use of the Borel-Serre boundary of the associated global symmetric space.
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Oct 30 Mon Mukul Tewary (Toronto) Mathematical Biology Seminar Series
14:00 Hicks LT 9 In vitro models of early developmental morphogenesis using human pluripotent stem cells
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Oct 31 Tue Nicola Franchini (Nottingham) Cosmology, Relativity and Gravitation
16:00 J11, Hicks Black Holes with Light Boson Hair and QPOs
 
  Abstract:
A complex bosonic field minimally coupled to gravity, can give rise to black holes solutions that evade the no-hair theorem. These solutions are spinning black holes that can be drastically different from Kerr ones. A phenomenological way to distinguish hairy and Kerr black holes is to measure the quasi-periodic oscillations, which are peaks in the X-ray flux , emitted in the inner region of the accretion disk. Interpreting these peaks with the relativistic precession model, one can predict the emission around hairy black holes. Future generation X-ray telescopes will be able to measure with high precision the quasi-periodic oscillations, hence giving a way to test the no-hair theorem.
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Nov 1 Wed Brita Nucinkis (University of London - Royal Holloway) Pure Maths Colloquium
14:00 J11 Finiteness conditions for classifying spaces for the family of virtually cyclic subgroups
 
  Abstract:

A conjecture of Juan-Pineda and Leary states that any group admitting a cocompact model for the classifying space for the family of virtually cyclic subgroups has to b be virtually cyclic already. This conjecture has been proved for large classes of groups.

In this talk I will give an overview of some of these results and constructions, will discuss a weakened condition for these spaces, and will give examples of groups satisfying this condition. This is joint work with N. Petrosyan.

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Nov 1 Wed Malte Heuer (Sheffield) ShEAF: postgraduate pure maths seminar
16:00 J11 Hicks Generalised complex geometry
 
  Abstract:
Generalised complex structures were introduced by Nigel Hitchin in 2003 and further developed by his student Marco Gualtieri. They give a unification of complex and symplectic geometry. We will see in which way these two seemingly very different structures can be thought of as extremal cases of generalised complex structures. The definition was motivated by phenomena in string theory, especially mirror symmetry where there is a link between symplectic and complex geometry.
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Nov 2 Thu Julian Holstein (Lancaster) Topology seminar
16:00 J11 Maurer-Cartan elements and infinity local systems
 
  Abstract:
Maurer-Cartan elements for differential graded Lie algebras or associative algebras play an important role in several branches of mathematics, in particular for classifying deformations . There are different sensible notions of equivalence for Maurer-Cartan elements, and while they agree in the nilpotent case, the general theory is not yet well-understood. This talk will compare gauge equivalence and different notions of homotopy equivalence for Maurer-Cartan elements of a dg-algebra. As an application we extend the study of cohesive modules introduced by Block, and find a new algebraic characterisation of infinity local systems on a topological space. This is joint work with Joe Chuang and Andrey Lazarev.
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Nov 3 Fri Fionnlagh Dover (University of Sheffield) SP2RC seminar
13:00 LT 11 MHD simulations of Jets with Applications to the Sun
 
  Abstract:
I will be presenting an overview of the open source software MPI-AMRVAC, with a focus on solar physical applications modelled by its inbuilt magnetohydrodynamic module. In particular, I have used this code for simulating MHD jets in gravitationally stratified atmospheres.
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Nov 3 Fri Akos Matszangosz Chromatic homotopy theory reading seminar
14:00 J11 Complex bordism - Part 2
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Nov 6 Mon Dimitar Kodjabachev HHR
15:00 J11 An introduction to the Arf-Kervaire invariant problem
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Nov 7 Tue Soheyla Feyzbakhsh (Edinburgh) Algebra / Algebraic Geometry seminar
14:00 J11 Reconstructing a K3 surface from a curve via wall-crossing
 
  Abstract:
In 1997, Mukai introduced a geometric program to reconstruct a K3 surface from a curve on that surface. The idea is to first consider a Brill-Noether locus of vector bundles on the curve. Then the K3 surface containing the curve can be obtained uniquely as a Fourier-Mukai partner of the Brill-Noether locus. Mukai carried out this program for curves of genus 11. I will explain how wall-crossing with respect to Bridgeland stability conditions implies that the Mukai's strategy works for curves of higher genera.
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Nov 7 Tue Theo Torres (Nottingham) Cosmology, Relativity and Gravitation
16:00 J11, Hicks Non-shallow water waves on a vortex: A model for dispersive fields around rotating black holes
 
  Abstract:
Shallow water waves scattering on a draining and rotating potential flow constitute the analogue of a rotating black hole. In such a spacetime, it has been shown theoretically that, at low frequency, waves can extract energy from black holes. Such a process in known as superradiance. Our recent observation of this effect in an experiment at the University of Nottigham (T.T. et al. Nature Phys. 13 (2017) 833-836 arXiv:1612.06180 [gr-qc]) suggests that superradiance persists beyond the shallow water regime. In this talk, I will present the experiment we conducted and I will extend some features of analogue rotating black holes to the dispersive regime. Especially I will focus on light rings and quasi-normal modes.
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Nov 9 Thu Arthur Gretton (UCL) Statistics Seminar
14:00
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Nov 9 Thu Constanze Roitzheim (Kent) Topology seminar
16:00 J11 K-local equivariant rigidity
 
  Abstract:
Equivariant stable homotopy concerns the study of objects with symmetry. It has been shown recently by Patchkoria that the G-equivariant stable homotopy category is uniquely determined by its triangulated structure, G-action and induction/transfer/restriction maps. In particular this implies that all reasonable categories of G-spectra realise the same homotopy theory. We consider this result with respect to equivariant K-theory, which merges model category techniques, equivariant structures and calculations from the stable homotopy groups of spheres.
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Nov 10 Fri Luca Pol Chromatic homotopy theory reading seminar
12:00 J11 The Adams spectral sequence
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Nov 10 Fri Matt Allcock (University of Sheffield) SP2RC seminar
13:00 LT 11 Solar magneto-seismology with asymmetric waveguides
 
  Abstract:
The Sun’s atmosphere, where magnetic forces dominate, is permeated by MHD waves that can be used as an indirect method for diagnosing difficult-to-measure parameters of solar plasma. This technique is known as solar magneto-seismology (SMS). In this talk, I will give a brief history of SMS development followed by a derivation of two novel techniques for SMS that use the asymmetry of the eigenmodes of asymmetric waveguides to estimate the strength of the background magnetic field, which is traditionally difficult to measure.
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Nov 13 Mon Natalia Petrovskaya (Birmingham) Mathematical Biology Seminar Series
14:00 Alfred Denny Conference Room Spatial patterns arising in a model of biological invasion with short-distance and long-distance dispersal.
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Nov 13 Mon Dimitar Kodjabachev HHR
15:00 J11 The Arf-Kervaire invariant problem - HHR proof strategy
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Nov 15 Wed Magdalini Flari (Sheffield) Differential geometry seminar
14:00 F38 Warps and grids for double and triple vector bundles (Despite the day and time, this is not the Pure Maths Colloquium.)
 
  Abstract:
Grids are a natural extension of the notion of section to double vector bundles. A grid consists of a pair of linear sections, and constitutes two non-commuting paths from the base manifold to the total space; the warp measures the lack of commutativity.

Well-known geometric objects can be expressed as warps: for example, the bracket of two vector fields is a warp, and, given a connection in a vector bundle, the covariant derivative of a section along a vector field is a warp.

In triple vector bundles, analysis of the six paths from the base manifold to the total space leads to identities among the warps of the constituent double vector bundles.

In this talk we will start with the concept of warp for double and triple vector bundles, build up to a general result for grids in triple vector bundles, and see some applications of this result for grids in the iterated tangent and cotangent bundles. This is joint work with Kirill Mackenzie.
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Nov 15 Wed Rebecca Hoyle (Southampton) Applied Mathematics Colloquium
14:00 Hicks, LT 9 Maternal effects and environmental change
 
  Abstract:
Maternal effects are influences of the maternal phenotype on offspring phenotypes by routes other than direct genetic transmission. Potentially they provide an additional means of adaptation to changing environmental conditions over and above that afforded by within-generation phenotypic plasticity. However, maternal effects have also been implicated in the risks of heart disease, diabetes and obesity. I will show how mathematical modelling can provide insight into the interaction of maternal effects and phenotypic plasticity under different patterns of environmental change and suggest when maternal effects might be expected to evolve and why.
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Nov 15 Wed Daniel Graves (Sheffield) ShEAF: postgraduate pure maths seminar
16:00 J11 Hicks A Simplicial View of Algebraic Topology
 
  Abstract:
Simplicial sets give a nice combinatorial model for topological spaces. In this talk I will introduce the foundations of the theory of simplicial sets and, time permitting, give some idea of how I use them in my own work
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Nov 16 Thu Timothy Waite (Manchester) Statistics Seminar
14:00
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Nov 16 Thu Sandra Palau (Bath) Probability
15:30 LT 7 Extinction properties and asymptotic behaviour of multi-type continuous state branching processes
 
  Abstract:
First, we will discuss how to construct multi-type continuous state branching processes. Under mild conditions, we will see that there exists a lead eigenvalue associated with the first-moment semigroup. The sign of this eigenvalue distinguishes between the cases where there is extinction and exponential growth. Finally, in the supercritical case, we will give the a.s. rate of growth and the convergence of the proportion of each type.
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Nov 16 Thu Markus Hausmann (Copenhagen) Topology seminar
16:00 J11 The Balmer spectrum of the equivariant homotopy category of a finite abelian group
 
  Abstract:
One of the basic tools to study a tensor-triangulated category is a classification of its thick tensor ideals. In my talk, I will discuss such a classification for the category of compact G-spectra for a finite abelian group G. This is joint work with Tobias Barthel, Niko Naumann, Thomas Nikolaus, Justin Noel and Nat Stapleton, and builds on work of Strickland and Balmer-Sanders.
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Nov 17 Fri Freddie Mather (University of Sheffield) SP2RC seminar
13:00 LT 11 Magneto-Acoustic Waves in the Stratified Solar Atmosphere: Single to Multi-Fluid Approach
 
  Abstract:
The solar atmosphere is a highly complex and structured media exhibiting stratification by gravity as well as containing many wave guide structures such as prominences. The temperature is also incredibly varied starting at around 5,000 K at the photosphere, dipping to 4,400 K at the temperature minimum and reaching the giddy heights of 1MK in the corona. Due to this temperature stratification the plasma may not be fully ionised in parts of the solar atmosphere. Much of the solar atmosphere is dynamic with flows following magnetic field lines readily observed. All of these must be taken into consideration when studying MHD waves in the solar atmosphere. In this talk we first consider the magneto-acoustic gravity (MAG) waves in a “vertical” field and study the energy distribution of the eigen-modes in two layer and single layer models of the solar atmosphere. Secondly we consider the effect of a constant bulk flow on the MAG surface waves given in Miles and Roberts (1992). The second part considers partial ionisation in slab structures such as prominences, in which bulk flows and the corresponding instabilities are considered.
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Nov 17 Fri Luca Pol Chromatic homotopy theory reading seminar
14:00 J11 Quillen's theorem
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Nov 21 Tue Fredrik Stromberg (Nottingham) Number Theory seminar
13:00 J11 Spectral theory and Maass forms for noncongruence subgroups
 
  Abstract:
The spectral theory for congruence subgroups of the modular group is fairly well understood since Selberg and the development of the Selberg trace formula. In particular it is known that congruence subgroups has an infinite number of discrete eigenvalues (corresponding to Maass cusp forms) and there is extensive support towards Selberg’s conjecture that there are no small eigenvalues for congruence subgroups. In contrast to this setting, much less is known for noncongruence subgroups of the modular group even though these groups are clearly arithmetic. In fact, it can be shown that under certain circumstances small eigenvalues must exist. And even the existence of infinitely many “new” discrete eigenvalues is not known for these groups. The main obstacle for developing the spectral theory here is that there is in general no explicit formula for the scattering determinant. In this talk I will present sufficient conditions for an “odd” discrete spectrum to exist and I will also give experimental support for the conjecture that these conditions are also necessary. I will also present an experimental version of Turing’s method for certifying correctness of the spectral counting.
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Nov 21 Tue Davide Masoero (Lisbon) Algebra / Algebraic Geometry seminar
14:00 J11 The isomonodromic deformation method for Painleve I and meromorphic functions with 5 transcendental singularities
 
  Abstract:
I will introduce the isomonodromic deformation method for Painleve I and the corresponding Riemann-Hilbert problem in term of Stokes multipliers. I will then use a theory due to R. Nevanlinna, [Ueber Riemannsche Flaechen mit endlich vielen Windungspunkten, Acta Math 1932] to give an alternative construction of the monodromy manifold, and a proof of the surjectivity of the monodromy map. Finally, I will comment on some applications of the same method to other Painleve equations: in particular, I will show how to compute the numer of real roots of the rational solutions of the fourth Painleve equations.
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Nov 22 Wed Jonathan Sherratt (Heriot-Watt) Applied Mathematics Colloquium
14:00 Hicks, LT 9 Using Mathematics to Infer the Historical Origin of Vegetation Patterns in Semi-Deserts
 
  Abstract:
Landscape-scale patterns of vegetation occur worldwide at interfaces between semi-arid and arid climates. They are important as potential indicators of climate change and imminent regime shifts, and arise from positive feedback between vegetation and infiltration of rainwater. On gentle slopes the typical pattern form is bands (stripes), oriented parallel to the contours, and their wavelength is probably the most accessible statistic for vegetation patterns. I will discuss the use of mathematical models to investigate different possible mechanisms for the origin of these patterns. I will show that patterns can arise either from degradation of uniform vegetation, or from the colonisation of bare ground. Most significantly, I will show that these two mechanisms can be distinguished by the relationship between pattern wavelength and slope gradient: degradation of uniform vegetation generates patterns whose wavelength increases with slope, while colonisation of bare ground gives the opposite trend. This makes it possible to infer the historical origin of the patterns. Specifically, for sub-Saharan Africa (the "Sahel" region) model predictions and historical rainfall data together imply that vegetation patterns originated by the colonisation of bare ground, either during c.1760-1790 or since c.1850.
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Nov 22 Wed Neil Hansford (Sheffield) ShEAF: postgraduate pure maths seminar
16:00 J11 Hicks A Whistle Stop Tour of C*-categories
 
  Abstract:
C*-categories are categories in the usual 'objects and arrows' sense, equipped with additional structure comparable with the more analytic C*-algebras. Familiar concepts from either side of the fence include norms, completeness, involutions, the C*-identity, morphism sets, (C*-) functors, and much more. We will have a brief overview of C*-categories, taking in their abstract definition, some specific examples, functors, representations, ideals and quotients, as well as the generalisation of an important construction from the world of C*-algebras.
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Nov 23 Thu Claudia Scheimbauer (Oxford) Topology seminar
16:00 J11 Fully extended functorial field theories and dualizability in the higher Morita category
 
  Abstract:
Atiyah and Segal's axiomatic approach to topological and conformal quantum field theories provided a beautiful link between the geometry of "spacetimes" (cobordisms) and algebraic structures. Combining this with the physical notion of "locality" led to the introduction of the language of higher categories into the topic. Natural targets for extended topological field theories are higher Morita categories: generalizations of the bicategory of algebras, bimodules, and homomorphisms. After giving an introduction to topological field theories, I will explain how one can use geometric arguments to obtain results on dualizablity in a ``factorization version’’ of the Morita category and using this, examples of low-dimensional field theories “relative” to their observables. An example will be given by polynomial differential operators, i.e. the Weyl algebra, in positive characteristic and its center. This is joint work with Owen Gwilliam.
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Nov 23 Thu Andrew Bell (Sheffield) RSS Seminar Series
16:30 Hicks LT9 Formula for success: multilevel modelling of Formula One driver and constructor performance
 
  Abstract:
Dr Bell will present to us on his paper which uses random-coefficient models and (a) finds rankings of who are the best formula 1 (F1) drivers of all time, conditional on team performance; (b) quantifies how much teams and drivers matter; and (c) quantifies how team and driver effects vary over time and under different racing conditions. The points scored by drivers in a race (standardised across seasons and Normalised) is used as the response variable in a cross-classified multilevel model that partitions variance into team, team-year and driver levels. These effects are then allowed to vary by year, track type and weather conditions using complex variance functions. Juan Manuel Fangio is found to be the greatest driver of all time. Team effects are shown to be more important than driver effects (and increasingly so over time), although their importance may be reduced in wet weather and on street tracks. A sensitivity analysis was undertaken with various forms of the dependent variable; this did not lead to substantively different conclusions. The paper argues that the approach can be applied more widely across the social sciences, to examine individual and team performance under changing conditions.
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Nov 24 Fri Nicola Bellumat Chromatic homotopy theory reading seminar
14:00 J11 Formal groups and heights
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Nov 27 Mon Philip Greulich (Southampton) Mathematical Biology Seminar Series
14:00 Alfred Denny Conference Room Mathematical modelling of clonal stem cell dynamics
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Nov 28 Tue Carl Wang-Erickson (Imperial) Number Theory seminar
13:00 J11 The rank of Mazur's Eisenstein ideal
 
  Abstract:
In his landmark 1976 paper "Modular curves and the Eisenstein ideal", Mazur studied congruences modulo p between cusp forms and an Eisenstein series of weight 2 and prime level N. He proved a great deal about these congruences, and also posed some questions: how big is the space of cusp forms that are congruent to the Eisenstein series? How big is the extension generated by their coefficients? In joint work with Preston Wake, we give an answer to these questions in terms of cup products (and Massey products) in Galois cohomology. We will introduce these products and explain what algebraic number-theoretic information they encode. Time permitting, we may be able to indicate some partial generalisations to square-free level.
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Nov 28 Tue Emilie Dufresne (Nottingham) Algebra / Algebraic Geometry seminar
14:00 J11 Separating invariants and local cohomology
 
  Abstract:
The study of separating invariants is a new trend in Invariant Theory and a return to its roots: invariants as a classification tool. For a finite group acting linearly on a vector space, a separating set is simply a set of invariants whose elements separate the orbits o the action. Such a set need not generate the ring of invariants. In this talk, we give lower bounds on the size of separating sets based on the geometry of the action. These results are obtained via the study of the local cohomology with support at an arrangement of linear subspaces naturally arising from the action. (Joint with Jack Jeffries)
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Nov 29 Wed Anna Barbieri (Sheffield) Pure Maths Colloquium
14:00 J11 Frobenius manifolds
 
  Abstract:

The notion of Frobenius structures was introduced by Dubrovin in the '90s as a geometric axiomatization of 2 dimensional Topological Field Theories. A Frobenius manifold is essentially a manifold whose tangent spaces at any point are endowed with the structure of associative Frobenius algebra, varying "smoothly" with respect to a metric. The associativity is encoded in a system of non-linear PDE called WDVV equations.

The talk is an introduction to Frobenius manifolds and to their link with the theory of isomonodromic deformations and with WDVV equations.

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Nov 29 Wed Ricardo Garcia-Mayoral (Cambridge) Applied Mathematics Colloquium
14:00 Hicks, LT 9 Alteration of near-wall turbulence by textured surfaces
 
  Abstract:
The structure of turbulence near walls can be altered by the presence of surface features such as roughness or texturing, providing opportunities to control the flow passively. The surface texture can induce a coherent component in the flow, as well as a shift in the 'virtual origin' experienced by the overlying turbulence. We will illustrate these mechanisms using the examples of transitionally rough and superhydrophobic textures.
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Nov 29 Wed Rudolf Chow (Sheffield) ShEAF: postgraduate pure maths seminar
16:00 J11 Hicks A Tale of Two Sieves
 
  Abstract:
Over 300 years ago, the French mathematician Mersenne conjectured that $2^{251} − 1$ was a composite number. This was finally proved 120 years ago, but even 50 years ago the computational load to actually factor the number was considered insurmountable -- the technology and theory at that time would have taken roughly $10^{20}$ years to do so. But this all changed with the advent of accessible and fast computing power as the number was factorised in 1984, merely taking 32 hours.

In this talk we will first discuss the method that was used, the quadratic sieve by Pomerance in 1981, before moving on to a more complicated yet powerful version of it, the number field sieve by Pollard in 1996. There'll be plenty of actual numbers and examples!
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Nov 30 Thu Neil Strickland (Sheffield) Topology seminar
16:00 J11 Thoughts on the Telescope Conjecture
 
  Abstract:
Ravenel's 1984 paper "Localization with respect to certain periodic theories" posed a series of highly prescient conjectures, most of which were later proved by Hopkins, Devinatz and Smith. These results form the heart of chromatic homotopy theory. One conjecture, called the Telescope Conjecture, remained unproven. It can be formulated in many ways, one of which is as follows: if $X$ is a spectrum such that $v_n^{-1}X$ is defined, and $BP_*(v_n^{-1}X)=0$, then already $v_n^{-1}X=0$. This is trivial for $n=0$, and is true for $n=1$ by a theorem of Miller. However, many people including Ravenel came to believe that it is probably false for $n\geq 2$. In 2000 Mahowald, Ravenel and Shick published a paper describing their attempt to disprove the conjecture. They constructed a certain spectral sequence, and showed that the conjecture would imply properties of the spectral sequence that they found implausible, but they were not able to complete the proof of impossibility.

This talk will survey this work, and present some small new ideas about properties of certain spectra $T(n,q)$ that play an important role here and in some related areas.
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Dec 1 Fri Dimitar Kodjabachev Chromatic homotopy theory reading seminar
14:00 J11 The stratification of M_FG
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Dec 4 Mon Akos Matszangosz HHR
16:00 J11 Real bordism
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Dec 5 Tue Ariel Weiss (Sheffield) Number Theory seminar
13:00 J11 Irreducibility of Galois representations associated to low weight Siegel modular forms
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Dec 5 Tue Gregory Stevenson (Glasgow) Algebra / Algebraic Geometry seminar
14:00 J11 A^1-homotopy invariants of singularity categories
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Dec 6 Wed Vladislav Vysotsky (University of Sussex) Pure Maths Colloquium
14:00 J11 Convex hulls of random walks
 
  Abstract:

Random convex polytopes have been extensively studied over the last decades. A popular model of such polytope is the convex hull of a random walk (which is a random sequence whose increments are independent random vectors with identical distribution). I will present a problem on such convex hulls with notable connections to conic geometry and combinatorics. This is a joint work with Zakhar Kabluchko (Munster) and Dmitry Zaporozhets (St. Petersburg).

Consider the probability that the convex hull of an n-step random walk in R^d does not absorb the origin, which in dimension one means that the trajectory of the walk does not change its sign. The remarkable formula of Sparre Andersen (1949) states that any one-dimensional random walk with symmetric continuous distribution of increments stays positive with probability (2n-1)!!/(2n)!!, which does not depend on the distribution. We prove a multidimensional distribution-free counterpart of this result and give an explicit tractable formula for the absorption probability. Our idea is to show that the absorption problem is equivalent to a geometric problem on counting the number of Weyl chambers of type B_n in R^n intersected by a generic linear subspace of co-dimension d. As the main application of this result, we obtain explicit distribution-free formulas for the expected number of faces and vertices of the convex hulls of the random walk.

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Dec 6 Wed Kenta Ishimoto (Oxford) Applied Mathematics Colloquium
14:00 Hicks, LT 9 Hydrodynamics of sperm rheotaxis and guidance of microswimmers
 
  Abstract:
Sperm cells swim against a flow -- just as salmon swimming in the river. This sperm rheotacic behaviour was first observed more than a century ago, and recently, it has been hypothesised to be a mechanism of sperm guidance in female reproductive tract. In this talk, we present simple hydrodynamic simulations and theoretical models that could explain this phenomenon, and proceed to consider mathematical structures of the hydrodynamic interactions of a microswimmer in a flow. Possible engineering applications for guidance of microswimmeres will also be discussed.
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Dec 6 Wed Di Zhang (Sheffield) ShEAF: postgraduate pure maths seminar
16:00 J11 Hicks Reciprocity laws and $L$-functions
 
  Abstract:
Hilbert's ninth problem was to prove the reciprocity law for $n$-th power residue for an arbitrary number field $K$ and for $n>2$, and it was partially solved by Emil Artin. How did Artin guess his reciprocity law? He was led to the law in trying to show that a new kind of L-function was a generalization of the usual L-function. In today's talk we will see why the factorization of some L-functions can be viewed as some form of ''reciprocity law''.
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Dec 7 Thu Maria Kalli (Kent) Statistics Seminar
14:00
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Dec 8 Fri Dr David Tsiklauri (Queen Mary's University London ) SP2RC seminar
13:00 LT 11 Alfven wave phase-mixing in flows: why over-dense solar coronal open magnetic field structures are cool? and phase mixing in ABC magnetic fields.
 
  Abstract:
We include the effect of plasma flow in Alfvén wave (AW) damping via phase mixing and explore the observational implications. We apply our findings [1] to addressing the question why over-dense solar coronal open magnetic field structures (OMFS) are cooler than the background plasma. Observations show that the over-dense OMFS (e.g. solar coronal polar plumes) are cooler than surrounding plasma and that, in these structures, Doppler line-broadening is consistent with bulk plasma motions, such as AW. If over-dense solar coronal OMFS are heated by AW damping via phase-mixing, we show that, co-directional with AW, plasma flow in them reduces the phase-mixing induced-heating, thus providing an explanation of why they appear cooler than the background. Also, briefly 3D MHD simulation of linearly polarised Alfven wave dynamics in Arnold-Beltrami-Childress magnetic field [2] will be discussed. [1] D. Tsiklauri, Astron. Astrophys. 586, A95 (2016) [2] D. Tsiklauri, Phys. Plasmas 21, 052902 (2014)
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Dec 12 Tue Marta Mazzocco (Loughborough) Algebra / Algebraic Geometry seminar
14:00 J11 Colliding holes in Riemann surfaces
 
  Abstract:
In 1997 Hitchin proved that the Riemann Hilbert correspondence between Fuchsian systems and conjugacy classes of representations of the fundamental group of the punctured sphere is a Poisson map. Since then, some generalisations of this result to the case of irregular singularities have been proposed by Boalch and by Gualtieri, Li and Pym. In this talk we interpret irregular singularities as the result of collisions of boundaries in a Riemann surface and show that the Stokes phenomenon corresponds to the presence of "bordered cusps". We introduce the concept of decorated character variety of a Riemann surface with bordered cusps and construct a generalised cluster algebra structure and cluster Poisson structure on it. We define the quantum cluster algebras of geometric type and show that they provide an explicit canonical quantisation of this Poisson structure.
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Dec 13 Wed Marco Schlichting (University of Warwick) Pure Maths Colloquium
14:00 J11 The Euler class of a projective module
 
  Abstract:
In topology, the existence of a nowhere vanishing section of an oriented vector bundle is detected by its Euler class (in case rank of vector bundle equals dimension of base). This is classical and goes back to at least the 1950s. The analogous story in algebra is less classical and has led to deep questions and results in algebraic K-theory, algebraic cycles, A1-homotopy and group homology. After recalling the topological story, I will give a survey of the algebraic side.
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Dec 13 Wed Ed Pearce (Sheffield) ShEAF: postgraduate pure maths seminar
16:00 J11 Hicks Jacobi's Identity and the Dirac Sea
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Dec 14 Thu Ostap Hryniv (Durham) Probability
14:00 LT 3 Limiting behaviour of self-avoiding polygons
 
  Abstract:
In the ensemble of two-dimensional self-avoiding polygons enclosing a fixed area (and centred at the origin), consider a probability distribution whose weights decay exponentially in polygon length. We study statistical properties of these polygons in the limit of large values of the enclosed area. Under a natural sub-criticality condition, we show that this probability distribution concentrates on a deterministic Wulff shape, derive a sharp asymptotics of the corresponding partition function, and describe the normal fluctuations of these polygons around the average profile.
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Dec 14 Thu Danny Sugrue (Queens University Belfast) Topology seminar
16:00 J11 The title is Rational Mackey functors of profinite groups.
 
  Abstract:
Rational Mackey functors for a compact topological group G are a useful tool for modelling rational G equivariant cohomology theories. Having a better understanding of Mackey functors will enhance our understanding of G-cohomology theories and G-equivariant homotopy theory in general. In the compact Lie group case, rational Mackey functors have been studied extensively by John Greenlees (and others). In this talk we will discuss what can be shown in the case where G is profinite (an inverse limit of finite groups).
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Jan 19 Fri Jordan Williamson Chromatic homotopy theory reading seminar
14:00 J11 The classification of formal groups
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Jan 26 Fri Scott Balchin Chromatic homotopy theory reading seminar
14:00 J11 Flat modules over M_FG
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