Torus actions on the Cuntz algebras, bundles,  and their reciprocal algebras.

Taro Sogabe (Kyoto University)
Thursday, 30th January 2025 15:10-16:00

Abstract:
In the operator algebra theory, it is often an interesting problem to find the torus  actions on an operator algebra and investigate their fixed point algebras.
The Cuntz algebra has a natural torus action whose fixed point algebra is the UHF algebra (i.e., infinite tensor product of the matrix algebra).
I would like to explain the Cuntz algebras and these torus actions, and I will introduce some problems related to the action including, the existence of some torus actions on the bundles of Cuntz algebras,  the position of the torus action in the fundamental group of the automorphism group of the Cuntz algebra.
If time permits, I will talk about a gauge action on the reciprocal Cuntz(–Krieger) algebras which was investigated in our ongoing joint work with Kengo Matsumoto.

Vinberg degeneration of Harish-Chandra transform

Roman Gonin (Cardiff University)
Thursday, 6th February 2025 15:10-16:00

Abstract:
Perverse sheaves play an important role in topology and algebraic geometry, with rich applications in Geometric Representation Theory (GRT). A key approach within GRT involves realising algebras and actions on K-theory. Omitting the K-theory functor leads naturally to a categorification. The Hecke algebra is fundamental in representation theory, particularly in the study of quantum groups. The monodromic Hecke category is a natural extension of its categorification.

In this talk, I will provide a gentle introduction to perverse sheaves, assuming no prior knowledge. We discuss the monodromic Hecke category, the Harish-Chandra transform as its categorical centre, and the Vinberg degeneration of the transform. The talk is based on a joint work with Kostiantyn Tolmachov and Andrei Ionov.

C*-algebraic factorization homology

Lucas Hataishi (University of Oxford)
Thursday, 13th February 2025 15:10-16:00

Abstract:
In this talk I will discuss an approach to analyze a class of framed 2-dimensional TQFTs arising from the representation theory of quasitriangular locally compact quantum groups.
The TQFTs are constructed via factorization homology with values in C*-categories, but its is expected that their values can be computed by means of actions of quantum groups on C*-algebras.
I will focus the exposition on the case of quasitriangular compact quantum groups, where the strategy can be fully implemented without being obscured by issues of analytical nature.

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Vanessa Miemietz (University of East Anglia)

Thursday, 20th February 2025 15:10-16:00

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Felix Schulze (University of Warwick)

Thursday, 27th February 2025 15:10-16:00

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Iolo Jones (Durham University)

Thursday, 6th March 2025 15:10-16:00

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Thomas Wasserman (University of Oxford)

Thursday, 13th March 2025 15:10-16:00

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Dinakar Muthiah (University of Glasgow)

Thursday, 20th March 2025 15:10-16:00

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Mike Hill (University of Minnesota)

Thursday, 8th May 2025 15:10-16:00