C6 | Mathematical Institute

Thu, 22 Oct 2026
11:00

Constructing models over a predicate

Martin Bays

(Oxford University)

Abstract

Given a complete theory T and a definable set X, we can consider the class of structures X(M) (with the induced structure) for M a model of T. When is this itself an elementary class, i.e. when does every model of the theory of the induced structure extend to a model of T? This "existence" property has been studied in particular in the context of Gaifman's conjecture that it is implied by relative categoricity, i.e. uniqueness over X of the model when it exists. I will discuss some of the history of this, and some work with Itay Kaplan and Pierre Simon which shows that this existence property holds if X is stably embedded and T is simple (or just rosy), going via X being what we call "arid".

Wed, 18 Nov 2026
11:30

TBC

Raz Slutsky

Abstract

to follow

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Wed, 11 Nov 2026
11:30

TBC

Randy Pham

Abstract

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Wed, 04 Nov 2026
11:30

TBC

Alexander Mylet, Samuel Gil, Lucas Yeung

Abstract

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Wed, 28 Oct 2026
11:30

Operator-Algebraic Methods for Categorical Symmetries

Yuhan Gai

Abstract

In quantum many-body systems and quantum field theories, the notion of symmetry extends beyond groups to include higher categorical structures. In one spatial dimension, finite symmetries of this kind are described by unitary fusion categories. One could ask: how can such symmetries be realised on lattice systems, and which symmetries admit such realisations?

In this talk, I will first review fusion categories, together with an operator-algebraic framework for these fusion category symmetries in 1+1d lattice models, proposed by Evans and Jones [arXiv:2507.05185]. I will then discuss a recent result of Bunner and Jones [arXiv:2605.21327], showing that every unitary fusion category can be realised on tensor products of Hilbert spaces, provided infinite-dimensional ancillary Hilbert spaces are allowed.

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Wed, 21 Oct 2026
11:30

An overview of a C*-algebraic ultrapower technique

Joseph Gondek

Abstract

In recent joint work with Felipe Flores, it was shown that the C*-algebra generated by the quasi-regular representation of Thompson's F < T is purely infinite. The proof involves an ultrapower technique developed by Robert and later considered by Ozawa. In this talk, we will discuss why ultrapowers are relevant in this context and how one works with them, focusing on a few proof techniques.

Wed, 14 Oct 2026
11:30

The one percent property for free groups

Ferdinand Jacobé de Naurois

Abstract

Kesten's theorem characterises amenability in terms of spectral radii: a symmetric random walk on a group G has spectral radius 1 if and only if it generates an amenable subgroup.

We prove a quantitative "1%" version of this result for G a free group, or a fully residually free group: for every ε > 0, there is δ > 0 such that for every probability measure μ on G with convolution operator norm at least ε, there is a co-set of an amenable subgroup of G of mass > δ under μ.

This answers a question of Emmanuel Breuillard. We believe the same result to hold in a broader setting of linear groups, with δ depending on the dimension. The proof uses uniform exactness and a generalisation of the Tits alternative.

Joint work with Emmanuel Breuillard.