Thu, 01 Oct 2020

16:00 - 17:00
Virtual

Systems Thinking and Problem Solving: Value-based Approaches to Mathematical Innovation (Cancelled)

Professor R. Eddie Wilson
(University of Bristol)
Further Information

More information on the Reddick Lecture.

Abstract

This talk is a personal how-to (and how-not-to) manual for doing Maths with industry, or indeed with government. The Maths element is essential but lots of other skills and activities are equally necessary. Examples: problem elicitation; understanding the environmental constraints; power analysis; understanding world-views and aligning personal motivations; and finally, understanding the wider systems in which the Maths element will sit. These issues have been discussed for some time in the management science community, where their generic umbrella name is Problem Structuring Methods (PSMs).

Tue, 17 Nov 2020

15:30 - 16:30
Virtual

Zeros, moments and derivatives

Nina Snaith
(University of Bristol)
Further Information

This seminar will be held via zoom. Meeting link will be sent to members of our mailing list (https://lists.maths.ox.ac.uk/mailman/listinfo/random-matrix-theory-anno…) in our weekly announcement on Monday.

Abstract

For 20 years we have known that average values of characteristic polynomials of random unitary matrices provide a good model for moments of the Riemann zeta function.  Now we consider moments of the logarithmic derivative of characteristic polynomials, calculations which are motivated by questions on the distribution of zeros of the derivative of the Riemann zeta function.  Joint work with Emilia Alvarez. 

Tue, 03 Nov 2020

15:30 - 16:30
Virtual

A threefold way to integrable probabilistic models

Thomas Bothner
(University of Bristol)
Further Information

This seminar will be held via zoom. Meeting link will be sent to members of our mailing list (https://lists.maths.ox.ac.uk/mailman/listinfo/random-matrix-theory-anno…) in our weekly announcement on Monday.

Abstract

This talk is intended for a broad math and physics audience in particular including students. It will focus on the speaker’s recent contributions to the analysis of the real Ginibre ensemble consisting of square real matrices whose entries are i.i.d. standard normal random variables. In sharp contrast to the complex and quaternion Ginibre ensemble, real eigenvalues in the real Ginibre ensemble attain positive likelihood. In turn, the spectral radius of a real Ginibre matrix follows a different limiting law for purely real eigenvalues than for non-real ones. We will show that the limiting distribution of the largest real eigenvalue admits a closed form expression in terms of a distinguished solution to an inverse scattering problem for the Zakharov-Shabat system. This system is directly related to several of the most interesting nonlinear evolution equations in 1 + 1 dimensions which are solvable by the inverse scattering method. The results of this talk are based on our joint work with Jinho Baik (arXiv:1808.02419 and arXiv:2008.01694)

Tue, 14 Jul 2020

15:30 - 16:30

Adiabatic invariants for the FPUT and Toda chains in the thermodynamic limit

Tamara Grava
(University of Bristol)
Abstract
We consider the Fermi-Pasta-Ulam-Tsingou (FPUT) chain composed by N particles  on the line  and endowed the phase space with the Gibbs measure at temperature 1/beta. We prove that the   integrals of motion of the Toda chain  are adiabatic invariants for the FPTU chain for times of order beta. Further we prove that certain combination of the harmonic energies are adiabatic invariants  of the FPUT chain  on the same time scale, while they are adiabatic invariants for Toda chain for all times. Joint work with A. Maspero, G. Mazzuca and A. Ponno.
Wed, 12 Feb 2020
16:00
C1

Generalising Mirzakhani’s curve counting result

Nick Bell
(University of Bristol)
Abstract

On any hyperbolic surface, the number of curves of length at most L is finite. However, it is not immediately clear how quickly this number grows with L. We will discuss Mirzakhani’s breakthrough result regarding the asymptotic behaviour of this number, along with recent efforts to generalise her result using currents.

Wed, 04 Mar 2020
16:00
C1

Automorphisms of free groups and train tracks

Monika Kudlinska
(University of Bristol)
Abstract


 Let phi be an outer automorphism of a free group. A topological representative of phi is a marked graph G along with a homotopy equivalence f: G → G which induces the outer automorphism phi on the fundamental group of G. For any given outer automorphism, the choice of topological representative is far from unique. Handel and Bestvina showed that sufficiently nice automorphisms admit a special type of topological representative called a train track map, whose dynamics can be well understood. 
In this talk I will outline the definition and motivation for train tracks, and give a sketch of Handel and Bestvina’s algorithm for finding them.
 

Thu, 12 Mar 2020

16:00 - 17:00
L5

Growth in soluble linear groups over finite fields

Brendan Murphy
(University of Bristol)
Abstract

In joint work with James Wheeler, we show that if a subset $A$ of $GL_n(\mathbb{F}_q)$ is a $K$-approximate group and the group $G$ it generates is soluble, then there are subgroups $U$ and $S$ of $G$ and a constant $k$ depending only on $n$ such that:

$A$ quickly generates $U$: $U\subseteq A^k$,
$S$ contains a large proportion of $A$: $|A^k\cap S| \gg K^{-k}|A|, and
$S/U$ is nilpotent.

Briefly: approximate soluble linear groups over any finite field are (almost) finite by nilpotent.

The proof uses a sum-product theorem and exponential sum estimates, as well as some representation theory, but the presentation will be mostly self-contained.

Thu, 23 Jan 2020

16:00 - 17:00
L5

Efficient congruence and discrete restriction for (x,x^3)

Kevin Hughes
(University of Bristol)
Abstract

We will outline the main features of Wooley's efficient congruencing method for the parabola. Then we will go on to prove new bounds for discrete restriction to the curve (x,x^3). The latter is joint work with Trevor Wooley (Purdue).

Wed, 11 Mar 2020

17:30 - 18:30
L1

Oxford Mathematics Public Lecture. Alan Champneys: Why pedestrian bridges wobble - synchronisation and the wisdom of the crowd

Alan Champneys
(University of Bristol)
Further Information

There is a beautiful mathematical theory of how independent agents tend to synchronise their behaviour when weakly coupled. Examples include how audiences spontaneously rhythmically applause and how nearby pendulum clocks tend to move in sync. Another famous example is that of the London Millennium Bridge. On the day it opened, the bridge underwent unwanted lateral vibrations that are widely believed to be due to pedestrians synchronising their footsteps.

In this talk Alan will explain how this theory is in fact naive and there is a simpler mathematical theory that is more consistent with the facts and which explains how other bridges have behaved including Bristol's Clifton Suspension Bridge. He will also reflect on the nature of mathematical modelling and the interplay between mathematics, engineering and the real world. 

Alan Champneys is a Professor of Applied Non-linear Mathematics at the University of Bristol. 

Please email @email to register.

Watch live:
https://twitter.com/OxUniMaths
https://www.facebook.com/OxfordMathematics/
https://livestream.com/oxuni/Champneys

The Oxford Mathematics Public Lectures are generously supported by XTX Markets.

Mon, 27 Jan 2020

16:00 - 17:00

Steklov eigenvalue problem on orbisurfaces

Asma Hassannezhad
(University of Bristol)
Abstract

 The Steklov eigenvalue problem is an eigenvalue problem whose spectral parameters appear in the boundary condition. On a Riemannian surface with smooth boundary, Steklov eigenvalues have a very sharp asymptotic expansion. Also, a number of interesting sharp bounds for the $k$th Steklov eigenvalues have been known. We extend these results on orbisurfaces and discuss how the structure of orbifold singularities comes into play. This is joint work with Arias-Marco, Dryden, Gordon, Ray and Stanhope.

Subscribe to University of Bristol