# Abstracts

05 October 2018: Agelos Georgakopoulos (Warwick) From mafia expansion to analytic functions in percolation theory
Abstract:
I will present a (finite) random graph model that admits various definitions, one of which is via a percolation model on an infinite group. This will lead us to an excursion into classical results and open problems in percolation theory.

12 October 2018: Robert Gilman (Stevens Institute) Generating the symmetric group
Abstract:
It is well known that two randomly chosen permutations generate the alternating or symmetric group of degree n with probability tending to 1 as n goes to infinity. This is bad news if you would like to sample 2-generator permutation groups. We study a sampling method which provably avoids this problem, and we discuss a practical heuristic variation.

19 October 2018: Joel Hamkins (Oxford) The rearrangement number: how many rearrangements of a series suffice to validate absolute convergence?
Abstract:
The Riemann rearrangement theorem asserts that a series $\sum_n a_n$ is absolutely convergent if and only if every rearrangement $\sum_n a_{p(n)}$ of it is convergent, and furthermore, any conditionally convergent series can be rearranged so as to converge to any desired extended real value. How many rearrangements $p$ suffice to test for absolute convergence in this way? The rearrangement number, a new cardinal characteristic of the continuum, is the smallest size of a family of permutations, such that whenever the convergence and value of a convergent series is invariant by all these permutations, then it is absolutely convergent. The exact value of the rearrangement number turns out to be independent of the axioms of set theory. In this talk, I shall place the rearrangement number into a discussion of cardinal characteristics of the continuum, including an elementary introduction to the continuum hypothesis and an account of Freiling's axiom of symmetry.

﻿26 October 2018: Andrzej Zuk (Paris 7 and Imperial) From PDEs to groups
Abstract:
We present a construction which associates to a KdV equation the lamplighter group. In order to establish this relation we use automata and random walks on ultra discrete limits. It is also related to the L2 Betti numbers introduced by Atiyah which are homotopy invariants of closed manifolds.

﻿2 November 2018: Dorothy Buck (Bath) Topological Effects -- and Treatments -- of Confined Biopolymers
Abstract:
DNA, like any other long piece of string packed into a small space, would become highly knotted and tangled if there were no mechanisms to both keep it organised, and to untangle any knots that do arise. Every living organism has developed mechanisms to control DNA knotting in its cells, and many antibiotics and chemotherapeutics act by disturbing this control. This talk will give an overview of some of the topological methods that we utilise to model DNA knotting in open chains, closed circles and spatial graphs, and how the answers from these models aid experimentalists. (No prior biological knowledge needed.)

﻿9 November 2018: Ed Brambley (Warwick) Mathematical modelling of aeroacoustics and metal forming
Abstract:
Aeroacoustics is the study of sound generated by airflow, typically in an aircraft engine but with applications to car noise and wind turbine noise, among others. This part of this talk will concentrate on models for acoustic linings that absorb sound. We will see how the model for the last 40 years is provably wrong (ill-posed), what we can do about it, and how even today we do not have a good predictive model for sound absorption by a surface in an airflow.

Metal Forming is bending bits of metal into the right shape. It is how most things from coke cans to cars are made. Finite element analysis is the tool of choice for engineers, but it is not fast enough for real-time control of metal forming processes; so these processes are not controlled. With a controlled metal forming process, we could make parts we can't today; we could reduce the energy needed to make parts; we could use more recycled metal; and, possibly, we could build machines that can make more than one part. The missing ingredient is a sufficiently accurate, sufficiently quick model of how metal forms, which is where mathematical modelling can help. This part of this talk will look at some recent attempts by my group at mathematical modelling of some simple metal forming processes.

﻿16 November 2018: Nathalie Wahl (Copenhagen and Newton Institute) Homological stability: what is that for?
Abstract:
Homological stability is a topological property shared by many configuration spaces and groups of matrices, or, more generally, groups of symmetries. In recent years, it has turned into a powerful computational tool. The talk will give an overview of the subject.

﻿23 November 2018: Impact colloquium - coordinated by Colm Connaughton

Join us for 3 short talks on research impact

1 - Sarah Hall - Why worry about making a difference? The impact agenda in higher education
Warwick’s new Head of Research Impact, Sarah Hall, will give a short presentation exploring various drivers for the impact agenda. This talk examines the question “Why should we be making a difference with research?” from national, institutional and personal perspectives.

2 - Colm Connaughton - Why buying a train ticket is NP-hard: ticket splitting and other mathematical problems in transportation systems
I will discuss some problems which have arisen from collaborations between the MathSys CDT and Thales UK on data-driven modelling and analysis of the UK’s transportation networks.

3 - Kat Rock - Modelling for elimination: integrating mathematical predictions with African sleeping sickness policy
I will outline how the BMGF-funded HAT Modelling & Economic Predictions for Policy project based at Warwick is working in conjunction with programme directors and strategy implementers to eliminate this deadly disease.

30 November 2018: Francesco Mezzadri ﻿(Bristol) Random Matrices, spectral moments and hypergeometric orthogonal polynomials
Abstract:
Spectral moments of random matrices have been extensively studied for almost forty years in many branches of mathematics and physics, like QCD, Quantum Transport, Number theory and Combinatorics. They continue to reveal an incredibly rich and varied mathematical structure. I will give an overview of the progress in the field over the past few years. In particular, I will discuss a fascinating recent discovery: the spectral moments of the classical random matrix ensembles are hypergeometric orthogonal polynomials belonging to the Askey scheme. This unifies different strands of current research and provides powerful analytical tools to study these quantities.

﻿07 December 2018: Alejandro Adem (British Columbia and Newton Institute) The Topology of Commuting Matrices
Abstract:
In this talk we will discuss the structure of spaces of commuting elements in a compact Lie group. Their connected components and other basic topological properties will be discussed. We will also explain how they can be assembled to produce a space which classifies certain bundles and represents an interesting cohomology theory. A number of explicit examples will be provided for orthogonal, unitary and projective unitary groups.