Vector-Valued Concentration on the Symmetric Group

Explore a groundbreaking vector-valued concentration inequality for the uniform measure on the symmetric group in this 45-minute lecture by Miriam Gordin from the Hausdorff Center for Mathematics. Delve into the significance of this novel result, which extends beyond the product setting of previously known inequalities. Examine the implications for the nonembeddability of the symmetric group into Banach spaces of nontrivial Rademacher type, a topic of interest in the metric geometry of Banach spaces. Learn how this work builds upon prior research by Ivanisvili, van Handel, and Volberg, who proved a vector-valued inequality on the discrete hypercube, addressing a question posed by Eno in the metric theory of Banach spaces. Gain insights into this collaborative research conducted with Ramon van Handel, expanding the understanding of vector-valued concentration inequalities beyond classical results in Gaussian measure on Rn and uniform measure on the discrete hypercube.