Five Warwick Maths Professors invited to speak at world-renowned ICM

Professor Karen Vogtmann

Karen Vogtmann's work is mainly in the areas of topology and geometric group theory. She is widely known for introducing new topological and geometric models for the study of infinite discrete groups, and has had a particularly strong influence on the modern approach to automorphism groups of free groups. Her work has connections to fields as diverse as the study of phylogenetic trees and perturbative quantum field theory, as well as to other areas of mathematics such as algebraic K-theory, homotopy theory, and tropical algebraic geometry.

Professor Vogtmann's honours and awards include the Polya prize of the London Mathematical Society, a Humboldt Research Prize, an honorary degree from the University of Copenhagen, an invited address at the 2006 International Congress of Mathematicians, and a plenary address at the 2016 European Congress of Mathematicians. She is a Fellow of the Royal Society, and a member of the US National Academy of Sciences, the American Academy of Arts and Sciences and Academia Europa. Before relocating to Warwick in 2014 she was the Goldwin Smith Professor of Mathematics at Cornell University.

ICM Emmy Noether Lecture

The Emmy Noether Lecture is a one-hour plenary lecture, honouring women who have made fundamental and sustained contributions to the mathematical sciences.

Karen will be presenting on the topic of spaces of graphs and a special commemorative plaquette will be presented to Karen.

Karen said: “I am very honoured and a bit intimidated, I just hope I can live up to the International Mathematical Union’s expectations for this lecture."

Professor Tim Austin

Tim Austin earned his PhD at the University of California, Los Angeles in 2010. After a Clay Research Fellowship, he has held positions at New York University, UCLA, and most recently the Warwick Mathematics Institute. His research touches on ergodic theory, probability and analysis. His recent work studies analogies between various modes of convergence for sparse graphs and for unitary group representations, and on notions of entropy that can be formulated in either context.

Field: Dynamics

Abstractly, a "dynamical system" is a mathematical structure that can be in a range of possible states and whose state changes according to some rule as time passes. Within this field, most of Prof. Tim Austin work is about notions of "entropy". Historically, these provide ways to measure the long-run "unpredictability" of a dynamical system. More recently, related ideas have appeared in other parts of mathematics, such as the study of systems whose "dynamics" is a more complicated collection of symmetries rather than the one-dimensional flow of time. The exact details of Tim's talk is yet to be confirmed, but his recent work has focused on how different kinds of entropy can be tailored to the study of different kinds of symmetries, and what it can tell us about their underlying structure.

Professor Adam Harper

Adam has been a Professor at the University of Warwick, since 2016. He won the SASTRA Ramanujan Prize in 2019; a Whitehead Prize from the London Mathematical Society in 2020; and a Frontiers of Science Award at the ICBS in 2024.

Adam's research interests are in number theory, especially analytic and probabilistic number theory, and related subjects. For the last few years, a major goal of his work has been to understand the size and distribution of sums of random multiplicative functions, and then see how far these results may be transferred to deterministic multiplicative functions like Dirichlet characters. A theme of this work is the use of ideas from the probabilistic theory of (critical) multiplicative chaos. Other subjects that he has worked on include the size of the Riemann zeta function on the critical line; the distribution of smooth numbers; the variance of sequences in arithmetic progressions; the "pretentious" approach to sums of multiplicative functions; prime number races; and the so-called inverse problem for the large sieve.

Field: Number Theory

Number theory studies questions like the distribution of prime numbers. This doesn't inherently seem to involve any randomness, but we have known for over 50 years that some probabilistic ideas (like random matrix theory) are closely connected to number theory. A big focus of his recent work, and the focus of Adam's talk, has been developing the connections between number theory and another part of probability/mathematical physics, called "multiplicative chaos". Using this connection, we can prove rigorously that some important number theoretic objects are unexpectedly a little bit smaller than we would have guessed. This extra cancellation has the potential to break the so-called squareroot barrier in various longstanding problems, like the distribution of the Mobius function (a cousin of the primes) in arithmetic progressions.

Dr Richard Montgomery

Richard Montgomery works primarily in Extremal and Probabilistic Combinatorics and is currently an Associate Professor (Reader) at the University of Warwick. He received his PhD at the University of Cambridge in 2015 under the supervision of Andrew Thomason, after which he spent time at Trinity College, Cambridge, and then the University of Birmingham. His work has been recognised by a 2024 European Mathematics Society prize, a Philip Leverhulme prize, and the European Prize in Combinatorics, and is currently supported by an ERC starting grant

Field: Combinatorics

Graphs are mathematical representations of networks, and are comprised of vertices (or nodes) with edges (or links) connecting them. Some very difficult and old conjectures about the properties of graphs are easy to state, but hard in part because they apply to every graph or graphs with only some very weak properties. Recently, progress in the area has been made by first finding within graphs a substructure with a property called 'sublinear expansion'. This property is very weak. This is good as substructures with this property can be essentially found in any graph. However, it is also bad as using such a weak property is a difficult and delicate task, and often not much can be done with it. In recent years, we have learnt increasing much about how to use this property to construct substructures in graphs. Richard's talk will discuss this and the progress that has been made using it.

Professor Nikolaos Zygouras

Nikolaos (Nikos) Zygouras grew up in Greece, where he did his undergraduate studies in the department of Electrical Engineering at the National Technical University of Athens. Subsequently, he had the privilege and honour of completing his PhD under the guidance of S.R.S. Varadhan at the Courant Institute, NYU. Since 2008 , he has been a faculty member at the University of Warwick, following postdoctoral positions at ETH-Zurich and USC. His research interests revolve around disordered systems, KPZ universality, random polymer models and their rich connections to various other areas of probability and mathematics in general, including stochastic analysis, Stochastic PDEs, integrable probability and algebraic combinatorics.

Nikos said: “I am deeply honoured and humbled to be invited to the International Congress of Mathematicians, a gathering where the most influential mathematical developments of the past four years are presented and where lifetime achievements, the impact of mathematics and the spirit of collaboration are celebrated. It will be immensely stimulating to engage with leading figures from across the entire spectrum of mathematics and to exchange ideas—not only about mathematical research, but also about the role of our science in today’s world and its challenges."

Field: Probability

Nikos will be presenting jointly with his close friends and collaborators Francesco Caravenna (Milan) and Rongfeng Sun (Singapore) on a series of works they began more than a decade ago here at Warwick aimed at understanding the effect that disorder may have on models of statistical mechanics; for example the understanding of whether and when impurities alter the properties of a magnetic material. Their efforts culminated three years ago in the construction of a novel continuous object, named the Critical Stochastic Heat Flow, which captures how heat and diffusion flow in disordered physical environments at a critical temperature of phase transition . Using ideas from probability theory and stochastic analysis, non-trivial and intriguing phenomena were revealed, for the first time at such a setting, sparking wider investigations and opening new mathematical and physical directions.