Tue, 28 Feb 2023
14:00
L6

A Lusztig-Shoji algorithm for quivers and affine Hecke algebras

Jonas Antor
(University of Oxford)
Abstract

Perverse sheaves are an indispensable tool in representation theory. Their stalks often encode important representation theoretic information such as composition multiplicities or canonical bases. For the nilpotent cone, there is an algorithm that computes these stalks, known as the Lusztig-Shoji algorithm. In this talk, we discuss how this algorithm can be modified to compute stalks of perverse sheaves on more general varieties. As an application, we obtain a new algorithm for computing canonical bases in certain quantum groups as well as composition multiplicities for standard modules of the affine Hecke algebra of $\mathrm{GL}_n$.

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Photo of exhibit with someone walking past

Cascading Principles - a major mathematically inspired exhibition by Conrad Shawcross

Oxford Mathematics is delighted to be hosting one of the largest exhibitions by the artist Conrad Shawcross in the UK. The exhibition, Cascading Principles: Expansions within Geometry, Philosophy, and Interference, brings together 40 sculptures realised by the artist over the last seventeen years. The artworks are placed in public and private areas, forming a web of relationships which emerge as the viewer moves through the building.

Helen Byrne wins Outstanding Supervisor Award

Congratulations to Helen who has won one of the MPLS Outstanding Supervisor Awards for 2022. This award "recognises that Helen has promoted and implemented an inclusive and welcoming environment in her research group, and her actions have created a place where researchers thrive and are able to achieve their ambitions with all the positive repercussions this generates."

New starter

Welcome to Charlotte Holmes who started on Monday as Apprentice Finance and Accounting Technician.

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