Lp-unconditional partitions of free group von Neumann algebras

Title：L^p-unconditional partitions of free group von Neumann algebras

Speaker：Tao Mei（Baylor University）

Time：Thursday, August17, 2023, 10:45-11:45

Location：Mingde Building B201-2

Abstract：_{Let Fn，2 ≤ n ≤ ∞, be the non-abelian free group of n-free generators, and be the subsets of Fn} ⁽ⁱ⁾ _{consisting of reduced words starting with the i-th generator.  The partition Fn = ∪1≤i≤nFn}⁽ⁱ⁾ _{∪{e} implies the well-known nonameanablility of Fn. In a recent joint work with E. Ricard, we show that this partition is unconditional with respect to the noncommutative L}^p_{-norm.This implies that the group von Neumann algebra of F∞ admits a L}^p_{-unconditional partition with infinitely many components that satisfy a geometrical paradoxical property. It is a mystery whether the group von} Neumann algebra of F₂ ( or Fn for any finite n) admits such a partition. In this talk, I wish to introduce recent progress in this direction. Part of the talk is based on joint works with Z. Liu, E.Ricard, Q. Xu, and S. Yin.