Thu, 12 Mar 2026
12:00 -
13:00
L3
OCIAM TBC
Tobias Grafke
(University of Warwick)
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Further Information
Tobias Grafke's research focuses on developing numerical methods and mathematical tools to analyse stochastic systems. His work spans applications in fluid dynamics and turbulence, atmosphere–ocean dynamics, and biological and chemical systems. He studies the pathways and occurrence rates of rare and extreme events in complex realistic systems, develops numerical techniques for their simulation, and quantifies how random perturbations influence long-term system behaviour.
Thu, 20 Nov 2025
12:00 -
13:00
C5
Existence and weak-strong uniqueness of measure solutions to Euler-alignment/Aw-Rascle-Zhang model of collective behaviour
Ewelina Zatorska
(University of Warwick)
Abstract
I will discuss the multi-dimensional Euler–alignment system with a matrix-valued communication kernel, which is motivated by models of anticipation dynamics in collective behaviour. A key feature of this system is its formal equivalence to a nonlocal variant of the Aw–Rascle–Zhang (ARZ) traffic model, in which the desired velocity is modified by a nonlocal gradient interaction. The global-in-time existence of measure solutions to both formulations, can be obtained via a single degenerate pressureless Navier–Stokes approximation. I will also discuss a weak–strong uniqueness principle adapted to the pressureless setting and to nonlocal alignment forces. As a consequence of these results we can rigorously justify the formal correspondence between the nonlocal ARZ and Euler–alignment models: they arise from the same inviscid limit, and the weak–strong uniqueness property ensures that, whenever a classical solution exists, both formulations coincide with it.
Thu, 30 Oct 2025
12:00 -
13:00
C5
Differentiation on metric spaces
Pietro Wald
(University of Warwick)
Abstract
Cheeger’s seminal 1999 paper initiated the study of metric measure spaces that admit a generalised differentiable structure. In such spaces, Lipschitz functions—real-valued and, in some cases, Banach-valued—are differentiable almost everywhere. Since then, much work has gone into determining the precise geometric and analytic conditions under which such structures exist. In this talk, I will give a brief overview of the theory and present new results from joint work with David Bate.
Mon, 27 Oct 2025
16:00
16:00
C3
On the distribution of very short character sums
Paweł Nosal
(University of Warwick)
Abstract
In their paper concerning quadratic residues Davenport and Erdős show that normalized sums of Legendre symbols $(\tfrac{n}{p})$ of suitable length $H(p) = p^{o(1)}$, with uniformly random starting point $X \in [0,...,p-1]$ obey the Central Limit Theorem, as the size of prime conductor goes to infinity.
Recently, Basak, Nath and Zaharescu proved that the CLT still holds, if we pick $X$ uniformly at random from $[0,...,(\log p)^A], A>1$ , set $H(p) = (\log p)^{o(1)}$ and take the limit along full density subset of primes.
In this talk, I will present a modification of their approach, inspired by the work of Harper on short character sums over moving intervals. This allows us to obtain the CLT of this type with $X$ uniformly random from $[0,...,g(p)]$ with practically arbitrary $g(p) \ll p^{\epsilon}$ for all $\epsilon >0$.
Thu, 27 Nov 2025
17:00
17:00
L3
Pfaffian Incidence Geometry and Applications
Martin Lotz
(University of Warwick)
Abstract
Pfaffian functions, and by extension Pfaffian and semi-Pfaffian sets, play a crucial role in various areas of mathematics, including o-minimal theory. Incidence combinatorics has recently experienced a surge of activity, fuelled by the introduction of the polynomial partitioning method of Guth and Katz. While traditionally restricted to simple geometric objects such as points and lines, focus has shifted towards incidence questions involving higher dimensional algebraic or semi-algebraic sets. We present a generalization of the polynomial partitioning method to semi-Pfaffian sets and illustrate how this leads to Pfaffian generalizations of classic results in incidence geometry, such as the Szemerédi-Trotter Theorem. Finally, we outline an application of semi-Pfaffian geometry and Khovanskii's bound to the robustness of neural networks.
Thu, 12 Jun 2025
12:00
12:00
C6
Recent progress on the structure of metric currents.
Emanuele Caputo
(University of Warwick)
Abstract
The goal of the talk is to give an overview of the metric theory of currents by Ambrosio-Kirchheim, together with some recent progress in the setting of Banach spaces. Metric currents are a generalization to the metric setting of classical currents. Classical currents are the natural generalization of oriented submanifolds, as distributions play the same role for functions. We present a structure result for 1-metric currents as superposition of 1-rectifiable sets in Banach spaces, which generalizes a previous result by Schioppa. This is based on an approximation result of metric 1-currents with normal 1-currents. This is joint work with D. Bate, J. Takáč, P. Valentine, and P. Wald (Warwick).
Tue, 10 Jun 2025
16:00
16:00
Random multiplicative functions and their distribution
Seth Hardy
(University of Warwick)
Abstract
Understanding the size of the partial sums of the Möbius function is one of the most fundamental problems in analytic number theory. This motivated the 1944 paper of Wintner, where he introduced the concept of a random multiplicative function: a probabilistic model for the Möbius function. In recent years, it has been uncovered that there is an intimate connection between random multiplicative functions and the theory of Gaussian Multiplicative Chaos, an area of probability theory introduced by Kahane in the 1980's. We will survey selected results and discuss recent research on the distribution of partial sums of random multiplicative functions when restricted to integers with a large prime factor.