Date/Time
Date(s) - 07/03/2025
3:30 pm - 4:30 pm

This is the 2024-25 Nelson lecture held annually in honour of our former colleague Evelyn Nelson.

Speaker: Dr. Julia Wolf, University of Cambridge

Julia Wolf is Professor of Pure Mathematics at the University of Cambridge, where she was both an undergraduate and a graduate student. After obtaining her PhD, she spent three years in the United States, with postdoctoral fellowships at the Institute for Advanced Study in Princeton and MSRI at Berkeley, followed by an assistant professorship at Rutgers University. Between 2010 and 2013, she held a Hadamard Associate Professorship at Ecole Polytechnique in Paris, and between 2013 and 2018, a Heilbronn Readership at the University of Bristol, where she served as Associate Chair of the Heilbronn Institute for Mathematical Research for three years.

Her research interests lie at the intersection of combinatorics, number theory, harmonic analysis, and more recently, model theory. As of 2024, her research is supported by an EPSRC Fellowship. In 2022 she was elected Chair of the British Combinatorial Committee and in 2016 she received the Anne Bennett Prize of the London Mathematical Society.

Location: Hamilton Hall, Room 305

Title: When is a mathematical object well-behaved?

Abstract: We will come at the question in the title from two different angles: first, from the viewpoint of model theory, a subject in which for over half a century the notion of “stability” has played a central role in describing tame behaviour; secondly, from the perspective of combinatorics, where so-called “regularity decompositions” have enjoyed a similar level of prominence in a range of finitary settings, with remarkable applications in additive number theory and theoretical computer science.

In recent years, these two fundamental motifs have been shown to interact in interesting ways. In particular, it has been shown that mathematical objects that are stable in the model-theoretic sense admit particularly well-behaved regularity decompositions. If time permits, I will explain how higher-order generalisations of regularity have pointed the way towards a long-sought generalisation of stability, opening up a new dimension of the model-theoretic classification picture.