# Seminars this semester

Series:

Sep 30 Mon Evgeny Shinder (Sheffield) Algebraic Geometry Learning Seminar
15:00 J11 K3 surfaces, 1. Introduction to K3 surfaces and distribution of the talks

Oct 1 Tue Paul Johnson (Sheffield) Algebra / Algebraic Geometry seminar
12:00 J11 Partitions and Hilbert Schemes of Points

Abstract:
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.

Oct 2 Wed Bartek Protas (McMaster/INI Cambridge) Applied Mathematics Colloquium
14:00 Hicks, LT 9 Maximum Amplification of Enstrophy in Navier-Stokes Flows and the Hydrodynamic Blow-Up Problem

Abstract:
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
15:00 J11, Hicks Quasi-normal modes and fermionic vacuum decay around a Kerr black hole

Abstract:
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 3 Thu Ulrich Pennig (Cardiff) Topology seminar
16:00 J11 Equivariant higher twisted K-theory of SU(n) via exponential functors

Abstract:
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 7 Mon Adel Betina, Evgeny Shinder Algebraic Geometry Learning Seminar
15:00 J11 K3 surfaces, 2 (Hodge structures)

Oct 8 Tue Dhruv Ranganathan (Cambridge) Algebra / Algebraic Geometry seminar
12:00 J11 A Mayer-Vietoris theorem for Gromov-Witten theory

Abstract:
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 9 Wed Xenia de la Ossa (University of Oxford) Pure Maths Colloquium
14:00 J11 Finding new geometric structures in string theory

Abstract:
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
15:00 J11, Hicks Accelerated Bayesian inference using deep learning

Abstract:
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 10 Thu Daniel Nóbrega-Siverio (Rosseland Centre for Solar Physics, University of Oslo) SP2RC seminar
10:00 Hicks Building E39 European Solar Physics Seminars: Nonequilibrium ionization and ambipolar diffusion in magnetic flux emergence processes

Abstract:
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
14:00 K14 Modelling latent processes in population abundance surveys using hidden Markov models

Abstract:
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
16:00 J11 Now that's what I call...homology theories for algebras

Abstract:
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
16:00 Room F28 (Hicks Building) Solar atmospheric magnetohydrodynamic wave modes in magnetic flux tubes of elliptical cross-sectional shape

Abstract:
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 14 Mon Jeremy Oakley (Sheffield) Statistics Seminar
13:00 LT 6 Deep Learning reading group: Chapter 6 from Goodfellow et al. (2016)

Abstract:
Discussion of Chapter 6 from "Deep Learning", by Goodfellow, Bengio and Courville https://www.deeplearningbook.org/

Oct 14 Mon George Moulantzikos, Evgeny Shinder Algebraic Geometry Learning Seminar
15:00 J11 K3 surfaces, 3 (more on Hodge structures and basic geometry of K3 surfaces)

Oct 15 Tue Jenny August (Max Planck Institute for Mathematics in Bonn) Algebra / Algebraic Geometry seminar
12:00 J11 The Stability Manifold of a Contraction Algebra

Abstract:
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
16:00 LT B Royal Statistical Society (RSS) Sheffield Local group seminar.

Abstract:
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 16 Wed Haluk Sengun (Sheffield) Pure Maths Colloquium
14:00 J11 A K-theoretic Selberg trace formula

Abstract:
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
14:00 Hicks, LT 9 Testing general relativity with gravitational wave observations: From numerical analysis to Bayesian statistics

Abstract:
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 17 Thu Pierrick Bousseau (ETH Zurich) Algebra / Algebraic Geometry seminar
15:00 J11 Quasimodular forms from Betti numbers

Abstract:
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
16:00 J11 Higher categorical structures in algebraic quantum field theory

Abstract:
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 21 Mon Raluca Eftimie (Dundee) Mathematical Biology Seminar Series
14:00 Hicks LT9

Oct 21 Mon Algebraic Geometry Learning Seminar
15:00 J11 K3 surfaces, 4

Oct 22 Tue Nick Sheridan (Edinburgh) Algebra / Algebraic Geometry seminar
12:00 J11 The Gamma and SYZ conjectures: a tropical approach to periods

Abstract:
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)
14:00 I12 SWAT/SP2RC Paper Club - Selected topical paper

Oct 22 Tue Thanasis Bouganis (Durham) Number Theory seminar
14:00 J11 Quaternionic modular forms and the Rankin-Selberg method

Abstract:
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 23 Wed Takashi Sakajo (Kyoto/INI Cambridge) Applied Mathematics Colloquium
14:00 Hicks, LT 9 Topological Flow Data Analysis - Theory and Applications

Abstract:
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
16:00 J11 Hicks An Introduction to the Periodic Table of n-Categories

Abstract:
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 24 Thu Petros Syntelis (Solar and Magnetospheric Theory Group, University of St Andrews) SP2RC seminar
10:00 E39 ESPOS: Eruptions and flaring activity in emerging quadrupolar regions

Abstract:
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
13:00 K14 Bloom's Taxonomy, or How to Get New Modules Approved by APSE

Abstract:
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
14:00 LT E Nonparametric Methods and Models with Uncertainty Propagation

Abstract:
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
16:00 J11 Homological Stability: Coxeter, Artin, Iawahori-Hecke

Abstract:
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
16:00 Room F28 (Hicks Building) The Solar Spicule Tracking Code (SSTC)

Abstract:
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 28 Mon Jeremy Oakley (Sheffield) Statistics Seminar
13:00 LT 6 Deep Learning reading group: 6.5-7.2 from Goodfellow et al. (2016)

Oct 28 Mon Algebraic Geometry Learning Seminar
15:00 J11 K3 surfaces, 5

Oct 29 Tue Noah Arbesfeld (Imperial College London) Algebra / Algebraic Geometry seminar
12:00 J11 K-theoretic Donaldson-Thomas theory and the Hilbert scheme of points on a surface

Abstract:
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)
13:00 Hicks, G07 SWAT/SP2RC Paper Club: Solar jets

Oct 30 Wed Natasha Morrison (University of Cambridge) Pure Maths Colloquium
14:00 J11 The typical structure of sets with small sumset

Abstract:
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
14:00 Hicks, LT 9 Solar flare forecasting models from the perspective of machine learning: past, present and future

Abstract:
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
15:00 J11, Hicks Scattering of gravitational waves by a neutron star

Abstract:
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
16:00 J11 Hicks Poisson Algebra (Maram Alossaimi)
An Introduction to the Theory of Elliptic Curve Cryptography (Lewis Combes)
Calabi-Yau algebras and superpotentials (Yirui Xiong)

Abstract:
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 31 Thu Tom Hutchcroft (Cambridge) Statistics Seminar
14:00 LT E Phase transitions in hyperbolic spaces

Abstract:
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
16:00 J11 A model structure of second kind on differential graded modules

Abstract:
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 https://arxiv.org/abs/1909.11399.

Nov 4 Mon Adriana Dawes (Ohio State) Mathematical Biology Seminar Series
14:00 Hicks LT9

Nov 4 Mon Algebraic Geometry Learning Seminar
15:00 J11 K3 surfaces, 6

Nov 5 Tue Ben Davison (Edinburgh) Algebra / Algebraic Geometry seminar
12:00 J11 Strong positivity for quantum cluster algebras

Abstract:
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)
14:00 I12 SWAT/SP2RC Paper Club - Selected topical paper

Nov 5 Tue Robert Kurinczuk (Imperial) Number Theory seminar
14:00 J11 Local Langlands in families

Abstract:
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 6 Wed Ana Khukhro (University of Cambridge) Pure Maths Colloquium
14:00 J11 Expander graphs and where to find them

Abstract:
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
14:00 Hicks, LT 9 Waves and turbulence in the solar corona and solar wind

Abstract:
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
15:00 J11, Hicks Scalar Fields in two dimensional de Sitter Space

Abstract:
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
16:00 J11 Hicks The Structure of Chevalley Groups over Local Fields.

Abstract:
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 7 Thu Anwar Ali Aldhafeeri (Plasma Dynamics Group, University of Sheffield) SP2RC seminar
10:00 E39 ESPOS: MHD wave modes in the solar magnetic flux tubes with elliptical cross-section

Abstract:
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
14:15 J11 Royal Statistical Society (RSS) Sheffield Local group seminar.
Pigeon-holes and mustard seeds: Growing capacity to use data for society

Abstract:
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
16:00 J11 The Witt vectors with coefficients

Abstract:
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
16:00 Room F28 (Hicks Building) Simulations of MHD waves in structured plasmas

Abstract:
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 11 Mon CANCELLED Statistics Seminar
13:00 LT 6 Deep Learning reading group

Nov 11 Mon Nebojsa Pavic (Sheffield) Algebraic Geometry Learning Seminar
15:00 J11 K3 surfaces, 7

Nov 13 Wed Tom Morley (SoMaS) Applied Mathematics Colloquium
14:00 Hicks, LT 9 A quantum tour of anti-de Sitter spacetime

Abstract:
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 14 Thu Greg Stevenson (Glasgow) Topology seminar
16:00 LT7 An introduction to derived singularities

Abstract:
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 18 Mon Rastko Skepnek (Dundee) Mathematical Biology Seminar Series
14:00 Hicks LT9

Nov 18 Mon Anna Barbieri Algebraic Geometry Learning Seminar
15:00 J11 K3 surfaces, 8

Nov 19 Tue Cathy Hsu (Bristol) Number Theory seminar
14:00 J11 Eisenstein congruences and an explicit non-Gorenstein R=T

Abstract:
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
14:00 I12 Quasi-locality and asymptotic expanders

Abstract:

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 20 Wed Jan Spakula (University of Southampton) Pure Maths Colloquium
14:00 J11 Quasi-locality and Property A

Abstract:

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
14:00 Hicks, LT 9 Liouville type theorems in the stationary Navier-Stokes and related equations

Abstract:
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 $$u(x)\to 0 \quad \text{as} \quad |x|\to 0 . \hspace{4.5cm} (2)$$ We also assume finiteness of the Dirichlet integral, $$\int_{\Bbb R^3} |\nabla u|^2 dx <+\infty. \hspace{5cm} (3)$$ 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
16:00 J11 Hicks Classifying 2-blocks with an elementary abelian defect group

Abstract:
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 21 Thu Julius Koza (Astronomical Institute, Slovak Academy of Sciences) SP2RC seminar
10:00 LT 9 ESPOS: Spectral diagnostics of cool flare loops observed by SST

Abstract:
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
12:00 J11 Stability conditions on the derived category of coherent systems and Brill-Noether theory

Abstract:
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
14:00 LT E Modelling reporting delays for disease surveillance data

Abstract:
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
16:00 J11 Non-trivial Massey products in moment-angle complexes

Abstract:
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
16:00 Room F28 (Hicks Building) A New Analysis Procedure for Detecting Periodicities within Complex Solar Coronal Arcades

Abstract:
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 22 Fri Barbara Bolognese (Sheffield) Algebraic Geometry Learning Seminar
13:30 J11 K3 surfaces, 9

Nov 22 Fri Eleonora Di Valentino (University of Manchester) Cosmology, Relativity and Gravitation
14:00 LT9, Hicks Cosmology in tension

Abstract:
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 28 Thu Fionnlagh Mackenzie-Dover (SP2RC/Sheffield)
14:00 LT10 SWAT/SP2RC Paper Club - Selected topical paper

Nov 28 Thu POSTPONED: Marcel Ortgiese (Bath) Statistics Seminar
14:00 LT E

Dec 2 Mon Katrina Lythgoe (Oxford) Mathematical Biology Seminar Series
14:00 Hicks LT9

Dec 3 Tue Dimitri Wyss (École Polytechnique Fédérale de Lausanne) Algebra / Algebraic Geometry seminar
12:00 J11 Non-archimedean and motivic integrals on the Hitchin fibration

Abstract:
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 4 Wed 1. Farhad Allian / 2. Hope Thackray (SoMaS) Applied Mathematics Colloquium
14:00 Hicks, LT 9 1. A New Analysis Procedure for Detecting Periodicities within Complex Solar Coronal Arcades 2. Fast Magnetohydrodynamic Modes of a Semi-cylindrical Waveguide

Abstract:
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
15:00 J11, Hicks Constraining the interacting vacuum model of dark energy

Abstract:
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 5 Thu Jeroen Sijsling (Ulm) Number Theory seminar
10:00 J11 Curves and their Jacobians in computer algebra

Abstract:
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
13:00 LT-9 Sparse bounds for Bochner-Riesz operators

Abstract:
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
14:00 LT 10 Aspects of high-dimensional inference

Dec 5 Thu Ieke Moerdijk (Utrecht/Sheffield) Topology seminar
16:00 J11 Labelled configuration spaces and a theorem of Segal

Abstract:
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
16:00 Room F28 (Hicks Building) Waves and seismology of pores

Abstract:
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 6 Fri Yirui Xiong (Sheffield) Algebraic Geometry Learning Seminar
14:00 J11 K3 surfaces, 10

Dec 9 Mon Yirui Xiong Algebraic Geometry Learning Seminar
15:00 J11 K3 surfaces, 11

Dec 10 Tue Sira Gratz (Glasgow) Algebra / Algebraic Geometry seminar
12:00 J11 Higher SL(k)-friezes

Abstract:
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
14:00 J11 Representations of p-adic groups

Abstract:
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 11 Wed Anitha Thillaisundaram (University of Lincoln) Pure Maths Colloquium
14:00 J11 Ramification structures for quotients of generalised Grigorchuk-Gupta-Sidki groups

Abstract:
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
15:00 LT-B Intersection theory of derived stacks

Abstract:
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
15:00 J11, Hicks Hydrodynamic simulations of rotating black holes

Abstract:
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

16:00 J11 Hicks TBA

Abstract:
TBA

Dec 12 Thu James Cranch (Sheffield) Teaching Lunch
13:00 LT6 Maths competitions, and the journey from school to university

Abstract:
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
14:00 LT E Simulation-Based Calibration (SBC)

Abstract:
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
16:00 J11

Dec 16 Mon Thomas Clay (Liverpool) Mathematical Biology Seminar Series
14:00 Hicks LT9

Dec 16 Mon Algebraic Geometry Learning Seminar
15:00 J11 K3 surfaces, 12

Dec 18 Wed Alexandr Buryak (Leeds) Algebra / Algebraic Geometry seminar
14:00 J11

Feb 5 Wed Axel Polaczek (University of Sheffield) Cosmology, Relativity and Gravitation
15:00 J11, Hicks