Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.
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, 04 Dec 2025
17:00
17:00
L3
Sharply k-homogeneous actions on Fraïssé structures
Robert Sullivan
(Charles University, Prague)
Abstract
Given an action of a group G on a relational Fraïssé structure M, we call this action *sharply k-homogeneous* if, for each isomorphism f : A -> B of substructures of M of size k, there is exactly one element of G whose action extends f. This generalises the well-known notion of a sharply k-transitive action on a set, and was previously investigated by Cameron, Macpherson and Cherlin. I will discuss recent results with J. de la Nuez González which show that a wide variety of Fraïssé structures admit sharply k-homogeneous actions for k ≤ 3 by finitely generated virtually free groups. Our results also specialise to the case of sets, giving the first examples of finitely presented non-split infinite groups with sharply 2-transitive/sharply 3-transitive actions.