# Events archive

## Conferences

### Models in Population Dynamics, Ecology, and Evolution (MPDEE) 2020

Date: Monday 20 April 2020 - Friday 24 April 2020

Location: College Court Conference Centre and Hotel, University of Leicester

Abstract: The meeting will consider applications of mathematical modelling to explore processes and mechanisms in various biological systems ranging from a cell to the human society. A special focus will be on the interplay between ecology and evolution across time and space. MPDEE’20 is also expected to explore similarities between modelling techniques traditionally applied in ecology and evolution and those used in other life sciences with the purpose to enhance interdisciplinary approaches and to stimulate further advances in population dynamics, ecology and evolution. The meeting will be an open forum for interaction between theoreticians and empirical biologists with the main goal of enhancing communication between the two groups to better link theories with empirical realities.

The conference is organised by Andrew Morozov and Sergei Petrovskii.

Learn more about ‘Models in Population Dynamics, Ecology, and Evolution (MPDEE) 2020’

### Maths Meets Arts Festival

Date: 6 - 9 July 2020

Location: University of Leicester

Abstract: The Maths meets Arts Tiger Team (MmATT) at the University of Leicester’s Institute of Advanced Studies will host the first Maths Meets Arts Online Festival between 6 and 9 July 2020. The four-day festival includes talks, activities and workshops sharing recent and ongoing collaborations between artists and mathematicians – with events for the whole family. All festival events are free and will be streamed to our Twitch channel and archived later on Youtube.

### Characteristic Polynomials of Random Unitary Matrices, Symmetric Polynomials, and Painlevé Equations

Date: Tuesday 24 March 2020

Time: 5.00pm

Location: Ken Edwards LT3, University of Leicester

Abstract: The moments of characteristic polynomials play a central role in Random Matrix Theory. They appear in many applications, ranging from quantum mechanics to number theory. The mixed moments of the characteristic polynomials of random unitary matrices, i.e. the joint moments of the polynomials and their derivatives, can be expressed recursively in terms of symmetric polynomials. These expressions are not easy to compute, however, and so this does not give an effective method for calculating the mixed moments in general. I shall describe a new, alternative evaluation, in terms of solutions of Painlevé differential equations, that facilitates their computation and which allows one to prove previous conjectures concerning their asymptotics when the matrices are large.

### Sixth Symposium on Compositional Structures

Date: Monday 16 December - Tuesday 17 December 2019

Location: University of Leicester

Abstract: The *Symposium on Compositional Structures* is a regular series of interdisciplinary meetings aiming to support the growing community of researchers interested in the phenomenon of compositionality, from both applied and abstract perspectives, and in particular where category theory serves as a unifying common language. The conference is organised by Simona Paoli, Roy Crole, Peter Guthmann, Andrew Smith.

Learn more about Sixth Symposium on Compositional Structures

### Heilbronn Institute for Mathematical Research Workshop (HIMR): Topological Methods in Group Representation Theory

Date: Tuesday 19 November - Friday 22 November

Location: University of Leicester

Abstract: The workshop is funded by the Heilbronn Institute for Mathematical Research (HIMR) and aims to bring together experts in algebraic topology and group representation theory to understand how these two subjects inform one another. The conference is organised by Frank Neumann and Jason Semeraro.

## Applied Maths Seminar Series

### Professor Claudia Schillings

Date: 26 November 2020

Time: 2.00pm

Location: Microsoft teams (please contact Dr Alberto Paganini (a.paganini@leicester.ac.uk) to be added to the teams group)

Title and Abstract: Optimization approaches for Bayesian inverse problems: Preconditioning integration methods in the small noise or large data limit.

The Bayesian approach to inverse problems provides a rigorous framework for the incorporation and quantification of uncertainties in measurements, parameters and models. We are interested in designing numerical methods which are robust with respect to the size of the observational noise, i.e., methods which behave well in case of concentrated posterior measures. The concentration of the posterior is a highly desirable situation in practice, since it relates to informative or large data. However, it can pose a computational challenge for numerical methods based on the prior measure. We propose to use the Laplace approximation of the posterior as the reference measure for the numerical integration and analyze the effciency of Monte Carlo methods based on it. This is joint work with Bjoern Sprungk, TU Freiberg, and Philipp Wacker, FAU.

### Dr Cecilia Pagliantini

Date: 12 November 2020

Time: 2.00pm

Location: Microsoft teams (please contact Dr Alberto Paganini (a.paganini@leicester.ac.uk) to be added to the teams group)

Title and Abstract: Structure preserving model order reduction of parameterized Hamiltonian systems

Parameterized differential equations are ubiquitous in applied science and are characterized by input parameters that describe possible variations in geometric configuration or physical properties of the modelled system. When real-time and many-query simulations of such problems are required, computational methods need to face prohibitively high computational costs to provide sufficiently accurate and stable numerical solutions. To address this issue, model order reduction techniques construct low-complexity high-fidelity surrogate models that allow rapid and accurate solutions under parameter variation. However, many challenges remain to secure the robustness and efficiency needed for the numerical approximation of nonlinear time-dependent problems. After a brief introduction to reduce order models, we will discuss reduced basis methods (RBM) for parameterized Hamiltonian dynamical systems describing nondissipative phenomena. In this case, traditional RBM do not guarantee the preservation of the geometric structure underlying the physical properties of the dynamics, like symmetries, invariants and conservation laws, and might lead to unphysical behaviours. In addition, the local low-rank nature of nondissipative dynamics requires large reduced bases to achieve sufficiently accurate approximations. To overcome these problems, we have developed nonlinear reduced basis methods that yield surrogate models characterized by evolving reduced phase spaces endowed with the geometric structure of the original dynamics.

### Post-processing in automated error control - **Dr Tristan Pryer (University of Bath)**

Date: Thursday 12 March 2020

Time: 2.00pm

Location: Michael Atiyah 119, University of Leicester

Abstract: Post-Processing techniques are often used in numerical simulations for a variety of reasons from visualisation purposes to designing superconvergent approximations through to becoming fundamental building blocks in constructing numerical schemes. Another application of these operators is that they are a very useful component in automated error control for approximations of partial differential equations (PDEs).

The talk is roughly divided into two parts, the first is concerned with finite difference type discretisations and how one can construct appropriate post-processors to allow for the automated error control of well known, well used schemes.

In the second part we move onto discontinuous Galerkin schemes. We introduce a class of post-processing operator that “tweaks” a wide variety of existing post-processing techniques to enable efficient and reliable a posteriori bounds to be proven. This ultimately results in optimal error control for all manner of reconstruction operators, including those that superconverge.

### Bayesian methods for population estimation and forecasting - Professor Jon Forster (University of Warwick)

Date: Thursday 20 February 2020

Time: 2.00pm

Location: Michael Atiyah 119, University of Leicester

Abstract: The estimation and forecasting of population composition presents a series of challenging statistical inference problems. Each of the three key components of population change, fertility, mortality and migration (briefly) will be discussed in this talk. I will particularly focus on methods for forecasting UK mortality rates for population and pension planning and the development of dynamic mixture models to account for changing fertility patterns. I will illustrate how the models are combined to produce UK population forecasts, together with quantification of the associated uncertainty, under various scenarios.

### Transporting densities along ray trajectories using a phase-space integral operator with a direction preserving discretisation - Professor David Chappell

Date: Thursday 6 February 2020

Time: 2.00pm

Location: Michael Atiyah 119, University of Leicester

Abstract: Phase-space integral operator models for transporting ray densities through complex two and three dimensional domains have recently been proposed, based on the Frobenius-Perron operator. The dependence of the density on the momentum (or equivalently direction) variable has typically been approximated using a basis expansion of orthogonal polynomials. This approach allows for the inclusion of directivity in the model, going beyond more conventional radiosity based methods. However, due to the finite basis approximation, numerical diffusion leads to an accumulation of error each time the integral operator is applied. This issue is particularly problematic for transporting densities through a mesh, since transmission from one cell to the next is modelled via successive applications of the integral operator. In this talk, the potential for a direction preserving discretisation procedure will be discussed in order to eliminate these errors.

### Iterative regularization methods for large-scale linear inverse problems - Dr Silvia Gazzola (University of Bath)

Date: Thursday 16 January 2020

Time: 2.00pm

Location: Michael Atiyah 119, University of Leicester

Abstract: Inverse problems are ubiquitous in many areas of Science and Engineering and, once discretized, they lead to ill-conditioned linear systems, often of huge dimensions: regularization consists in replacing the original system by a nearby problem with better numerical properties, in order to find a meaningful approximation of its solution. After briefly surveying some standard regularization methods, both iterative (such as many Krylov methods) and direct (such as Tikhonov method), this talk will introduce a recent class of methods that merge an iterative and a direct approach to regularization. In particular, strategies for choosing the regularization parameter and the regularization matrix will be emphasized, eventually leading to the computation of approximate solutions of Tikhonov problems involving a regularization term expressed in some p-norms.

### Applied Modelling of the Human Pulmonary System - Dr David Kay (University of Oxford)

Date: Thursday 23 January 2020

Time: 2.00pm

Location: Michael Atiyah 119, University of Leicester

Abstract: In this work we will attempt, via virtual models, to interpret how structure and body positioning impact upon the outcomes of Multi-Breath-Washout tests.By extrapolating data from CT images, a virtual reduced dimensional airway/vascualr network will be constructed. Using this network both airway and blood flow profiles will be calculated. These profiles will then be used to model gas transport within the lungs. The models will allow us to investigate the role of airway restriction, body position during testing and washout gas choice have on MBW measures.

### The Nonlinear Eigenvalue Problem - Dr Stefan Güttel (University of Manchester)

Date: Thursday 30 January 2020

Time: 2.00pm

Location: Michael Atiyah 119, University of Leicester

Abstract: Given a matrix-valued function F which depends nonlinearly on a scalar variable z, the basic nonlinear eigenvalue problem consists of finding those z for which F(z) is singular. Such problems arise in many areas of computational science and engineering, including acoustics, control theory, fluid mechanics, and structural engineering. In this lecture I will give an introduction to nonlinear eigenvalue problems and some of their interesting mathematical properties. I will discuss applications and recent developments in algorithms for their solution.

### Collective phenomena in oscillator networks - Professor Antonio Politi (University of Aberdeen)

Date: Thursday 13 February 2020

Time: 2.00pm

Location: Michael Atiyah 119, University of Leicester

Abstract: It is well known that ensembles of oscillators can mutually synchronize, a phenomenon well embodied by the Kuramoto model. It is less clear how the microscopic (single oscillator) dynamics correlate with the macroscopic (collective) evolution; in particular we still do not know under which conditions a collective irregular dynamics can manifest itself. I will discuss a series of different models/setups, characterized by different degrees of self-sustained macroscopic dynamics. Starting from an early (artificial) model of globally coupled logistic maps, I will review more realistic ensembles of Stuart-Landau oscillators, as well different kinds of pulse coupled oscillators which are quite relevant in the context of neuroscience. The role of heterogeneity and sparseness of the connectivity are some of the ingredients that will be touched.

## Pure Maths Seminar Series

More details about previous seminars can be found here

### Sets where a typical Lipschitz function is somewhere differentiable - Michael Wemyss (University of Glasgow)

Date: Tuesday 3 March 2020

Time: 2.00pm

Location: Michael Atiyah 119, University of Leicester

Abstract: The first half of the talk will give a brief overview of intersection hyperplane arrangements inside Tits cones of both finite and affine Coxeter groups. Surprisingly, little seems to be known about them, and they exhibit quite strange behaviour! For example, we obtain precisely 16 tilings of the plane, with only 3 being the "traditional" Coxeter tilings.

These new hyperplane arrangements turn out to be quite fundamental. Algebraically, they (1) describe the exchange graph of certain "modifying modules", which should be thought of as maximal rigid objects, (2) classify all noncommutative resolutions for cDV singularities, and (3) classify tilting theory for (contracted) preprojective algebras. They also have many geometric consequences, but I will talk about these less. The main point, and motivation, is that these hyperplane arrangements describe the stability manifold for an arbitrary 3-fold flop X --> Spec R, where X can have terminal singularities, and thus they describe the Stringy Kahler Moduli Space.

Parts of the talk are joint with Iyama, parts with Hirano, and parts with Donovan

### Algebraic and combinatorial decompositions of Fuchsian groups - Daniel Labardini-Fragoso (UNAM, Mexico)

Date: Tuesday 21 January 2020

Time: 2.00pm

Location: Michael Atiyah 119, University of Leicester

Abstract: The discrete subgroups of PSL_2(R) are often called 'Fuchsian groups'. For Fuchsian groups \Gamma whose action on the hyperbolic plane H is free, the orbit space H/\Gamma has a canonical structure of Riemann surface with a hyperbolic metric, whereas if the action of \Gamma is not free, then H/\Gamma has a structure of 'orbifold'. In the former case, there is a direct and very clear relation between \Gamma and the fundamental group \pi_1(H/\Gamma,x): a theorem of the theory of covering spaces states that they are isomorphic. When the action of \Gamma is not free, the relation between \Gamma and \pi_1(H/\Gamma,x) is subtler. A 1968 theorem of Armstrong states that there is a short exact sequence 1->E->\Gamma->\pi_1(H/\Gamma,x)->1, where E is the subgroup of \Gamma generated by the elliptic elements. For \Gamma finitely generated, non-elementary and with at least one parabolic element, I will present full algebraic and combinatorial decompositions of \Gamma in terms of \pi_1(H/\Gamma,x) and a specific finitely generated subgroup of E, thus improving Armstrong's theorem.

This talk is based on an ongoing joint project with Sibylle Schroll and Yadira Valdivieso-Díaz that aims at describing the bounded derived categories of skew-gentle algebras in terms of curves on surfaces with orbifold points of order 2.

### Weierstrass type representations - Mason Pember (Politecnico di Torino, Italy)

Date: Tuesday 28 January 2020

Time: 2.00pm

Location: Michael Atiyah 119, University of Leicester

Abstract: In the 19th century, Weierstrass and Enneper developed a representation formula for minimal surfaces in Euclidean 3-space. This formula has been fundamental in the creation of many interesting examples of minimal surfaces. Since then several similar representations have been developed for other classes of surfaces in 3 dimensional space forms such as constant mean curvature 1 surfaces in hyperbolic 3-space. All of these representations have the same basic ingredients: a meromorphic function and a holomorphic 1-form. It is therefore natural to ask if these representations can be unified in some way. In this talk we will outline a unified geometric way of viewing these representations via the transformation theory of Omega surfaces.

### Quasi-Compact Group schemes and their representations - Pedro Luis del Ángel Rodríguez (CIMAT, Mexico)

Date: Tuesday 4 February 2020

Time: 2.00pm

Location: Michael Atiyah 119, University of Leicester

Abstract: We will start with a brief review of the classical representation theory for finite groups and recall the notion of topological group as well as the notion of group scheme and affine group scheme. We develop a representation theory for extensions of an abelian variety by an affine group scheme. We characterize the categories that arise as such a representation theory, generalizingin this way the classical theory of Tannaka Duality established for affine group schemes.

### Frieze mutations - Ana García-Elsener (UNMdP, Argentina)

Date: Tuesday 11 February 2020

Time: 2.00pm

Location: Michael Atiyah 119, University of Leicester

Abstract: Frieze is a lattice of positive integers satisfying certain rules. Friezes of type A were first studied by Conway and Coxeter in 1970’s, but they gained fresh interest in the last decade in relation to cluster algebras, that are generated via a combinatorial rule called mutation. Moreover, the categorification of cluster algebras developed in 2006 yields a new realization of friezes in terms of representation theory of algebras. In this new theory a frieze is an array of positive integers on the Auslander-Reiten quiver of a cluster tilted algebra such that entries on a mesh satisfy a unimodular rule. In this talk, we will discuss friezes of type A and D, and their mutations.

### Cluster varieties and toric varieties associated to fans - Alfredo Nájera (UNAM, Mexico)

Date: Tuesday 18 February 2020

Time: 2.00pm

Location: Michael Atiyah 119, University of Leicester

Abstract: Cluster varieties are algebraic varieties over the complex numbers constructed gluing algebraic tori using distinguished birational maps called cluster transformations. In a seminal work Gross-Hacking-Keel-Kontsevich introduced the scattering diagram associated to a cluster variety. Every such diagram is a fan in a real vector space endowed with certain additional information attached to each co-dimension 1 cone (the wall crossing automorphisms). The purpose of this talk is to explain how scattering diagrams can be used to construct partial compactifications of cluster Poisson varieties and toric degenerations of such. In this talk we will provide various of the definitions needed for the next talk by T. Magee.

### Cluster varieties and toric varieties associated to polytopes - Timothy Magee (University of Birmingham)

Date: Tuesday 18 February 2020

Time: 3.15pm

Location: Michael Atiyah 119, University of Leicester

Abstract: Cluster varieties are a relatively new, broadly interesting class of geometric objects that generalize toric varieties. In the previous talk Alfredo discussed how cluster Possion varieties partially compactify by a fan construction. In this talk we will see that their mirrors-- cluster A-varieties-- compactify by a polytope construction. Projective toric varieties are defined by convex lattice polytopes. I'll explain how convexity generalizes to the cluster world, where "polytopes" live in a tropical space rather than a vector space and "convex polytopes" define projective compactifiactions of cluster varieties. Time permitting, I'll conclude with two exciting applications of this more general notion of convexity: 1) an intrisic version of Newton-Okounkov bodies and 2) a possible cluster version of a classic toric mirror symmetry construction due to Batyrev. Based on joint work with Man-Wai Cheung and Alfredo Nájera Chávez.

### Sets where a typical Lipschitz function is somewhere differentiable - Olga Maleva (University of Birmingham)

Date: Tuesday 25 February 2020

Time: 2.00pm

Location: Michael Atiyah 119, University of Leicester

Abstract: This talk is devoted to the study of properties of Lipschitz functions, mainly between finite-dimensional spaces, and especially their differentiability properties. The classical Rademacher Theorem guarantees that every Lipschitz function between finite-dimensional spaces is differentiable almost everywhere. This means that every set of positive Lebesgue measure in a Euclidean space contains points of differentiability of every Lipschitz function defined on the whole space.A major direction in geometric measure theory research of the last two decades was to explore to what extent this is true for Lebesgue null sets. Even for real-valued Lipschitz functions, there are null subsets S of R^n (with n>1) such that every Lipschitz function on R^n has points of differentiability in S; one says that S is a universal differentiability set (UDS). Moreover, for some sets T which are not UDS, meaning that some bad Lipschitz function is nowhere differentiable in T, it may happen that a typical Lipschitz function has many points of differentiability in T. In a recent joint work with M. Dymond we give a complete characterisation of such sets: these are the sets which cannot be covered by an F-sigma 1-purely unrectifiable set. We also show that for all remaining sets a typical 1-Lipschitz function is nowhere differentiable, even directionally, at each point. In this talk I will present the latest results on UDS and the dichotomy of typical differentiability sets.