Speaker：Adrián Manuel González Pérez（Universidad Autónoma de Madrid）

Time：2025-8-19 16:30

Location：Conference Room S102 at Experiment Building at Haiyun Campus

Abstract:

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.