Recent developments on Schur multipliers

：Adrián Manuel González Pérez（西班牙马德里自治大学）
：2025-08-19 16:30
：海韵园实验楼S102

报 告 人：Adrián Manuel González Pérez（西班牙马德里自治大学）

时  间：2025年8月19日16:30

地  点：海韵园实验楼S102

内容摘要:

Schur multipliers are linear maps with a deceptively simple definition: Given a matrix, a Schur multiplier acting on it is a cell-wise multiplication operator. Despite this simplicity, establishing mapping properties of these operators between Banach spaces of matrices, like Schatten classes, has an extremely wide range of applications. For instance, they have been used as a key ingredient in Sukochev's solution of Krein's conjecture in the perturbation theory of linear operators. The relationship between Fourier and Schur multipliers, proven by Neuwirth and Ricard, gives an even more surprising connection with rigidity problems in group theory. Indeed, they played a key role in Lafforgue and de la Salle proof on the failure of the approximation property for Lp spaces of higher rank Lie groups. Advances in the optimal smoothness condition for certain Schur multipliers would lead to new group invariants that are both stable under W*-equivalence and that remember the rank of the Lie group.

个人简介：

Born in Madrid in 1988, Adrián Manuel González Pérez is currently a research fellow at the Autonomous University of Madrid. His work lays around the intersection of harmonic analysis in groups and von Neumann algebras. In particular, he has long been interested in the analysis on the noncommutative Lp spaces of the von Neumann algebra of a group and how geometrical group properties shape analytic results there. More recently, he has also taken interest in the (yet unknown) optimal mapping properties of certain multiparametric ergodic theorems.

 

联系人：宋翀