Tue, 08 Nov 2022

14:00 - 15:00
L5

On the Ryser-Buraldi-Stein conjecture

Richard Montgomery
(University of Warwick)
Abstract

A Latin square of order n is an n by n grid filled with n different symbols so that every symbol occurs exactly once in each row and each column, while a transversal in a Latin square is a collection of cells which share no row, column or symbol. The Ryser-Brualdi-Stein conjecture states that every Latin square of order n should have a transversal with n-1 elements, and one with n elements if n is odd. In 2020, Keevash, Pokrovskiy, Sudakov and Yepremyan improved the long-standing best known bounds on this conjecture by showing that a transversal with n-O(log n/loglog n) elements exists in any Latin square of order n. In this talk, I will discuss how to show, for large n, that a transversal with n-1 elements always exists.

Tue, 15 Nov 2022

15:30 - 16:30
L6

Unitary Brownian motion, 2D log-correlated field and loop soups

Isao Sauzzede
(University of Warwick)
Abstract

I will present two examples of log-correlated fields in 2 dimensions. It is well known that the log-characteristic polynomial of a uniform unitary matrix converges toward a 1 dimensional log-correlated field, and our first example will be obtained from a dynamical version of this model. The second example will be obtained from a radically different construction, based on the Brownian loop soup that we will introduce. It will lead to a whole family of log-correlated fields. We will focus on the description of the behaviour of these objects, more than on rigorous details.

Mon, 31 Oct 2022
14:15
L5

Closed Ricci Flows with Singularities Modeled on Asymptotically Conical Shrinkers

Max Stolarski
(University of Warwick)
Abstract

Shrinking Ricci solitons are Ricci flow solutions that self-similarly shrink under the flow. Their significance comes from the fact that finite-time Ricci flow singularities are typically modeled on gradient shrinking Ricci solitons. Here, we shall address a certain converse question, namely, “Given a complete, noncompact gradient shrinking Ricci soliton, does there exist a Ricci flow on a closed manifold that forms a finite-time singularity modeled on the given soliton?” We’ll discuss work that shows the answer is yes when the soliton is asymptotically conical. No symmetry or Kahler assumption is required, and so the proof involves an analysis of the Ricci flow as a nonlinear degenerate parabolic PDE system in its full complexity. We’ll also discuss applications to the (non-)uniqueness of weak Ricci flows through singularities.

Fri, 25 Nov 2022

12:00 - 13:00
N3.12

Knutson's Conjecture on the Representation Ring

Diego Martin Duro
(University of Warwick)
Abstract

Donald Knutson proposed the conjecture, later disproven and refined by Savitskii, that for every irreducible character of a finite group, there existed a virtual character such their tensor product was the regular character. In this talk, we disprove both this conjecture and its refinement. We then introduce the Knutson Index as a measure of the failure of Knutson's Conjecture and discuss its algebraic properties.

Mon, 08 Feb 2021

15:45 - 16:45
Virtual

Veering triangulations and related polynomial invariants

Anna Parlak
(University of Warwick)
Abstract

Veering triangulations are a special class of ideal triangulations with a rather mysterious combinatorial definition. Their importance follows from a deep connection with pseudo-Anosov flows on 3-manifolds. Recently Landry, Minsky and Taylor introduced a polynomial invariant of veering triangulations called the taut polynomial. During the talk I will discuss how and why it is connected to the Alexander polynomial of the underlying manifold.  

Thu, 26 May 2022

14:00 - 15:00
L3

Propagation and stability of stress-affected transformation fronts in solids

Mikhail Poluektov
(University of Warwick)
Abstract

There is a wide range of problems in continuum mechanics that involve transformation fronts, which are non-stationary interfaces between two different phases in a phase-transforming or a chemically-transforming material. From the mathematical point of view, the considered problems are represented by systems of non-linear PDEs with discontinuities across non-stationary interfaces, kinetics of which depend on the solution of the PDEs. Such problems have a significant industrial relevance – an example of a transformation front is the localised stress-affected chemical reaction in Li-ion batteries with Si-based anodes. Since the kinetics of the transformation fronts depends on the continuum fields, the transformation front propagation can be decelerated and even blocked by the mechanical stresses. This talk will focus on three topics: (1) the stability of the transformation fronts in the vicinity of the equilibrium position for the chemo-mechanical problem, (2) a fictitious-domain finite-element method (CutFEM) for solving non-linear PDEs with transformation fronts and (3) an applied problem of Si lithiation.

Mon, 25 Apr 2022
14:15
L5

Ricci flows with nonstandard initial data

Peter Topping
(University of Warwick)
Abstract

Most Ricci flow theory takes the short-time existence of solutions as a starting point and ends up concerned with understanding the long-time limiting behaviour and the structure of any finite-time singularities that may develop along the way. In this talk I will look at what you can think of as singularities at time zero. I will describe some of the situations in which one would like to start a  Ricci flow with a space that is rougher than a smooth bounded curvature Riemannian manifold, and some of the situations in which one considers smooth initial data that is only achieved in a non-smooth way. A particularly interesting and useful case is the problem of starting a Ricci flow on a Riemann surface equipped with a measure. I will not be assuming expertise in Ricci flow theory. Parts of the talk are joint with either Hao Yin (USTC) or ManChun Lee (CUHK).

Mon, 23 May 2022
14:15
L5

Ancient solutions and translators in Lagrangian mean curvature flow

Felix Schulze
(University of Warwick)
Abstract

For almost calibrated Lagrangian mean curvature flow it is known that all singularities are of Type II. To understand the finer structure of the singularities forming, it is thus necessary to understand the structure of general ancient solutions arising as potential limit flows at such singularities. We will discuss recent progress showing that ancient solutions with a blow-down a pair of static planes meeting along a 1-dimensional line are translators. This is joint work with J. Lotay and G. Szekelyhidi.

Tue, 03 May 2022

14:00 - 14:30
L3

Permutation compressors for provably faster distributed nonconvex optimization

Rafal Szlendak
(University of Warwick)
Abstract
In this talk, we are going to explore our recent paper that builds upon MARINA -- the current state-of-the-art distributed non-convex optimization method in terms of theoretical communication complexity. Theoretical superiority of this method can be largely attributed to two sources: the use of a carefully engineered biased stochastic gradient estimator, which leads to a reduction in the number of communication rounds, and the reliance on independent stochastic communication compression operators, which leads to a reduction in the number of transmitted bits within each communication round. In this paper we
 
i) extend the theory of MARINA to support a much wider class of potentially correlated compressors, extending the reach of the method beyond the classical independent compressors setting,  
 
ii) show that a new quantity, for which we coin the name Hessian variance, allows us to significantly refine the original analysis of MARINA without any additional assumptions, and 
 

iii) identify a special class of correlated compressors based on the idea of random permutations, for which we coin the term PermK. The use of this technique results in the strict improvement on the previous MARINA rate. In the low Hessian variance regime, the improvement can be as large as √n, when d > n, and 1 + √d/n, when n<=d, where n is the number of workers and d is the number of parameters describing the model we are learning.

Tue, 30 Nov 2021

14:00 - 15:00
Virtual

FFTA: Graph hierarchy: a novel framework to analyse hierarchical structures in complex networks

Choudhry Shuaib
(University of Warwick)
Further Information

This session will be virtual only. 

Abstract

Trophic coherence, a measure of a graph’s hierarchical organisation, has been shown to be linked to a graph’s structural and dynamical aspects such as cyclicity, stability and normality. Trophic levels of vertices can reveal their functional properties, partition and rank the vertices accordingly. Trophic levels and hence trophic coherence can only be defined on graphs with basal vertices, i.e. vertices with zero in-degree. Consequently, trophic analysis of graphs had been restricted until now. In this talk I will introduce a novel  framework which can be defined on any simple graph. Within this general framework, I'll illustrate several new metrics: hierarchical levels, a generalisation of the notion of trophic levels, influence centrality, a measure of a vertex’s ability to influence dynamics, and democracy coefficient, a measure of overall feedback in the system. I will then discuss what new insights are illuminated on the topological and dynamical aspects of graphs. Finally, I will show how the hierarchical structure of a network relates to the incidence rate in a SIS epidemic model and the economic insights we can gain through it.

Article link: https://www.nature.com/articles/s41598-021-93161-4

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