Mon, 12 May 2025
14:15
L5

Tight contact structures and twisted geodesics

Michael Schmalian
(Mathematical Institute (University of Oxford))
Abstract

Contact topology and hyperbolic geometry are two well-established, yet so far largely unrelated subfields of 3-manifold topology. We will discuss a recent result relating phenomena in these two fields. Specifically, we will demonstrate that tightness of certain contact structures on hyperbolic manifolds is detected by the behaviour of geodesics in the underlying hyperbolic geometry. A key geometric tool we will discuss is the deformation theory for hyperbolic manifolds. 

Tue, 13 May 2025
14:00
L6

Stacky interpretation of D-cap modules

Arun Soor
(University of Oxford)
Abstract

I will construct a fully-faithful functor from the category of co-admissible D-cap modules of Ardakov—Wadsley, to the category of quasi-coherent sheaves on the "analytic de Rham space”, at least in the case when the rigid variety is affinoid and étale over a polydisk. 

On the Regge behaviour of the AdS Virasoro-Shapiro amplitude
Alday, L Nocchi, M Virally, C Zhou, X Journal of High Energy Physics volume 2025 issue 4 (09 Apr 2025)

Our next Public Lecture (see item above) stars  Gábor Domokos, discoverer of the Gömböc. So, as a taster, here is Sam Howison explaining what exactly Gábor was up to.

Thu, 22 May 2025
16:00
C3

Convergence of unitary representations of discrete groups

Michael Magee
(University of Durham)
Abstract

Let G be an infinite discrete group; e.g. free group, surface groups, or hyperbolic 3-manifold group.

Finite dimensional unitary representations of G of fixed dimension are usually very hard to understand. However, there are interesting notions of convergence of such representations as the dimension tends to infinity. One notion — strong convergence — is of interest both from the point of view of G alone but also through recently realized applications to spectral gaps of locally symmetric spaces. For example, this notion bypasses (unconditionally) the use of Selberg's Eigenvalue Conjecture in obtaining existence of large area hyperbolic surfaces with near-optimal spectral gaps. 

The talk is a broadly accessible discussion on these themes, based on joint works with W. Hide, L. Louder, D. Puder, J. Thomas, R. van Handel.

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