Location: Room G07, Fry Building, School of Mathematics, University of Bristol
Dinner: Zero degrees (microbrewery restaurant)
11:00 – 11:50: Indira Chatterji (Laboratoire J.A. Dieudonné de l'Université de Nice)
12:00 – 12:30: Ryan O’Loughlin (University of Reading)
12:30 – 14:00: Lunch break
14:00 – 14:50: Marius Dadarlat (Purdue University)
15:00 – 15:20: Estelle Boffy (Laboratoire de mathématiques de Besançon)
15:20 – 15:50: Coffee/tea
15:50 – 16:20: Greg Patchell (University of Oxford)
16:30 – 16:50: Pénélope Azuelos (University of Bristol)
16:50 – 17:00: Break
17:00 – 17:50: Andrew Toms (Purdue University)
18:15 -TBD Drinks and dinner at Zero Degrees
Abstract
Ryan O’Loughlin - The Numerical Range as a Spectral Set
Crouzeix’s Conjecture is an open conjecture which claims that the operator norm of a polynomial applied to a matrix is bounded above by 2 times supremum of the polynomial over the numerical range of the matrix. In this talk I will first give a historical background on Crouzeix’s Conjecture starting from the von Neumann inequality, and then present some new recently published results on the conjecture.
Greg Patchell - Selfless Inclusions of C*-Algebras and Quantum Groups
Recently, strong asymptotic freeness, or selflessness, in C*-algebras has emerged as a powerful technique to prove important regularity properties including simplicity, unique trace, stable rank 1, and strict comparison. In particular, in Fall 2024, Amrutam, Gao, Kunnawalkam Elayavalli, and I showed that the reduced group C*-algebras of all hyperbolic groups with trivial finite radical are selfless, which resolved the open problem of strict comparison for the reduced group C*-algebra of the free group on two generators. Since then, our result has been expanded to include a much larger class of groups. Work has also begun on isolating selflessness for C*-algebras not arising from groups, including the result of Hayes, Kunnawalkam Elayavalli, and Robert on selflessness of the reduced free product of a large class of C*-algebras. I will introduce the general notion of a selfless inclusion of C*-algebras, with which we will see the selflessness of the unitary compact quantum groups. This work is joint with Ben Hayes, Srivatsav Kunnawalkam Elayavalli, and Leonel Robert.