Tue, 03 Jun 2025
16:00

The Fourier coefficients of the holomorphic multiplicative chaos

Joseph Najnudel
(University of Bristol)
Abstract

In this talk, we consider the coefficients of the Fourier series obtained by exponentiating a logarithmically correlated holomorphic function on the open unit disc, whose Taylor coefficients are independent complex Gaussian variables, the variance of the coefficient of degree k being theta/k where theta > 0 is an inverse temperature parameter. In joint articles with Paquette, Simm and Vu, we show a randomized version of the central limit theorem in the subcritical phase theta < 1, the random variance being related to the Gaussian multiplicative chaos on the unit circle. We also deduce, from results on the holomorphic multiplicative chaos, other results on the coefficients of the characteristic polynomial of the Circular Beta Ensemble, where the parameter beta is equal to 2/theta. In particular, we show that the central coefficient of the characteristic polynomial of the Circular Unitary Ensembles tends to zero in probability, answering a question asked in an article by Diaconis and Gamburd.

Wed, 19 Feb 2025
17:00
Lecture Theatre 1

The Mathematics of Wound Healing - Tanniemola Liverpool

Tanniemola Liverpool
(University of Bristol)
Further Information

Wound healing is a highly conserved process required for survival of an animal after tissue damage. Tannie will describe how we are beginning to use a combination of mathematics, physics and biology to disentangle some of the organising principles behind the complex orchestrated dynamics that lead to wound healing.

Tanniemola Liverpool is a Professor in the Applied Mathematics Institute of the School of Mathematics at Bristol.

Please email @email to register to attend in person.

The lecture will be broadcast on the Oxford Mathematics YouTube Channel on Wednesday 12 March at 5-6pm and any time after (no need to register for the online version).

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

Wed, 30 Oct 2024
16:00
L6

Counting subgroups of surface groups

Sophie Wright
(University of Bristol)
Abstract

The fundamental group of a hyperbolic surface has an infinite number of rank k subgroups. What does it mean, therefore, to pick a 'random' subgroup of this type? In this talk, I will introduce a method for counting subgroups and discuss how counting allows us to study the properties of a random subgroup and its associated cover.

Tue, 03 Dec 2024
16:00
L6

Large deviations of Selberg’s CLT: upper and lower bounds

Emma Bailey
(University of Bristol)
Abstract

Selberg’s CLT informs us that the logarithm of the Riemann zeta function evaluated on the critical line behaves as a complex Gaussian. It is natural, therefore, to study how far this Gaussianity persists. This talk will present conditional and unconditional results on atypically large values, and concerns work joint with Louis-Pierre Arguin and Asher Roberts.

Thu, 31 Oct 2024

12:00 - 13:00
L3

Volcanic fissure localisation and lava delta formation: Modelling of volcanic flows undergoing rheological evolution

Jesse Taylor-West
(University of Bristol)
Abstract
In this talk, I will present two volcanologically motivated modelling problems.  In the first, I will detail how thermoviscous localisation of volcanic eruptions is influenced by the irregular geometry of natural volcanic fissures. Fissure eruptions typically start with the opening of a linear fissure that erupts along its entire length, following which activity localises to one or more isolated vents within a few hours or days. Previous work has proposed that localisation can arise through a thermoviscous fingering instability driven by the strongly temperature dependent viscosity of the rising magma. I will show that, even for relatively modest variations of the fissure width, a non-planar geometry supports strongly localised steady states, in which the wider parts of the fissure host faster, hotter flow, and the narrower parts of the fissure host slower, cooler flow. This geometrically-driven localisation is different from, and typically more potent than, the thermoviscous fingering localisation observed in planar geometries.  
 
The second problem concerns lava delta formation. A lava delta arises when a volcanic lava flow enters a body of water, extending the pre-eruption shoreline via the creation of new, flat land. A combination of cooling induced rheological changes and the reduction in gravitational driving forces controls the morphology and evolution of the delta. I will present shallow-layer continuum models for this process, highlighting how different modes of delta formation manifest in different late-time behaviours.
Tue, 03 Dec 2024
15:00
L6

Short loxodromics in graph products

Alice Kerr
(University of Bristol)
Abstract
Let G be a finitely generated group, with finite generating set S. Suppose G contains elements with some property that we’re interested in.  Can we find elements with this property uniformly quickly in G? That is, does S^n contain an element with this property for a bounded n?
 
We will discuss this question for graph products, where the elements we are looking for are ones with nice hyperbolic properties, such as loxodromic and Morse elements. We will also talk about consequences for the growth of these groups. This is joint work with Elia Fioravanti.

 
Mon, 29 Apr 2024
16:00
L2

New Lower Bounds For Cap Sets

Fred Tyrrell
(University of Bristol)
Abstract

A cap set is a subset of $\mathbb{F}_3^n$ with no solutions to $x + y + z = 0$ other than when $x = y = z$, or equivalently no non-trivial $3$-term arithmetic progressions. The cap set problem asks how large a cap set can be, and is an important problem in additive combinatorics and combinatorial number theory. In this talk, I will introduce the problem, give some background and motivation, and describe how I was able to provide the first progress in 20 years on the lower bound for the size of a maximal cap set. Building on a construction of Edel, we use improved computational methods and new theoretical ideas to show that, for large enough $n$, there is always a cap set in $\mathbb{F}_3^n$ of size at least $2.218^n$. I will then also discuss recent developments, including an extension of this result by Google DeepMind.

Wed, 14 Feb 2024
17:00
Lecture Theatre 1

Logging the World - Oliver Johnson

Oliver Johnson
(University of Bristol)
Further Information

During the pandemic, you may have seen graphs of data plotted on strange-looking (logarithmic) scales. Oliver will explain some of the basics and history of logarithms, and show why they are a natural tool to represent numbers ranging from COVID data to Instagram followers. In fact, we’ll see how logarithms can even help us understand information itself in a mathematical way.

Oliver Johnson is Professor of Information Theory in the School of Mathematics at the University of Bristol. His research involves randomness and uncertainty, and includes collaborations with engineers, biologists and computer scientists. During the pandemic he became a commentator on the daily COVID numbers, through his Twitter account and through appearances on Radio 4 and articles for the Spectator. He is the author of the book Numbercrunch (2023), which is designed to help a general audience understand the value of maths as a toolkit for making sense of the world.

Please email @email to register.

The lecture will be broadcast on the Oxford Mathematics YouTube Channel on Wednesday 06 March at 5-6pm and any time after (no need to register for the online version).

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

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Wed, 01 Nov 2023

16:00 - 17:00
L6

Topology and dynamics on the space of subgroups

Pénélope Azuelos
(University of Bristol)
Abstract

The space of subgroups of a countable group is a compact topological space which encodes many of the properties of its non-free actions. We will discuss some approaches to studying the Cantor-Bendixson decomposition of this space in the context of hyperbolic groups and groups which act (nicely) on trees. We will also give some conditions under which the conjugation action on the perfect kernel is highly topologically transitive and see how this can be applied to find new examples of groups (including all virtually compact special groups) which admit faithful transitive amenable actions. This is joint work with Damien Gaboriau.

Thu, 16 Nov 2023
16:00
L5

90 years of pointwise ergodic theory

Ben Krause
(University of Bristol)
Abstract

This talk will cover the greatest hits of pointwise ergodic theory, beginning with Birkhoff's theorem, then Bourgain's work, and finishing with more modern directions.

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