Centralisers of linear growth automorphisms of free groups
Andrew, N
Martino, A
Mathematical Proceedings of the Cambridge Philosophical Society
volume 177
issue 2
219-240
(20 Sep 2024)
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
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)