New starter

Felix Tellander, Postdoctoral Research Associate in Mathematical Physics: N1.02

Fri, 31 May 2024

12:00 - 13:00
Quillen Room

The Hecke category

Jonas Antor
((University of Oxford))
Abstract

The Hecke category first rose to prominence through the proof of the Kazhdan-Lusztig conjecture. Since then, the Hecke category has proven to be a fundamental object in representation theory with many interesting applications to modular representation theory, quantum groups, knot theory, categorification and diagrammatic algebra. This talk aims to give a gentle introduction to the Hecke category. We will first discuss the geometric incarnation of the Hecke category and how it was used to prove the Kazhdan-Lusztig conjecture. Then, we move on to a more modern approach due to Soergel and Elias-Williamson which is purely algebraic, and we will discuss some recent advances in representation theory based on this approach.

Exploiting dynamic bifurcation in elastic ribbons for mode skipping and selection
 Huang, W Yu, T Vella, D Hsia, K Liu, M Journal of the Mechanics and Physics of Solids volume 190 (04 Jun 2024)
Thu, 06 Jun 2024
16:30
C2

The invariant subspace problem

Per Enflo
Abstract
I will present a method to construct invariant subspaces - non-cyclic vectors - for a general operator on Hilbert space. It represents a new direction of a method of "extremal vectors", first presented in Ansari-Enflo [1]. One looks for an analytic function l(T) of T, of minimal norm, which moves a vector y near to a given vector x. The construction produces for most operators T a non-cyclic vector, by gradual approximation by almost non-cyclic vectors. But for certain weighted shifts, almost non-cyclic vectors will not always converge to a non-cyclic vector. The construction recognizes this, and when the construction does not work, it will show, that T has some shift-like properties.

 

Reference:
1. S. Ansari, P. Enflo, "Extremal vectors and invariant subspaces", Transactions of Am. Math. Soc. Vol. 350 no.2, 1998, pp.539–558
Semi-chiral operators in 4d N = 1 gauge theories
 Budzik, K Gaiotto, D Kulp, J Williams, B Wu, J Yu, M Journal of High Energy Physics volume 2024 issue 5 (22 May 2024)
Wed, 17 Jul 2024
18:15
Science Museum, London SW7

Oxford Mathematics London Public Lecture: The Potential for AI in Science and Mathematics - Terence Tao. SOLD OUT

Terence Tao
(University of California, Los Angeles )
Further Information

Terry Tao is one of the world's leading mathematicians and winner of many awards including the Fields Medal. He is Professor of Mathematics at the University of California, Los Angeles (UCLA). Following his talk Terry will be in conversation with fellow mathematician Po-Shen Loh.

Please email @email to register to attend in person. Please note this lecture is in London.

The lecture will be broadcast on the Oxford Mathematics YouTube Channel on Wednesday 7th August at 5pm and any time after (no need to register for the online version). 

The Oxford Mathematics Public Lectures are generously supported by XTX Markets.

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