Banach--Mazur distance to the cube

Series
High Dimensional Seminar
Time
Wednesday, August 29, 2018 - 12:55pm for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Konstantin Tikhomirov – GeorgiaTech
Organizer
Konstantin Tikhomirov

We show that there is a symmetric n-dimensional convex set whose Banach--Mazur distance to the cube is bounded below by n^{5/9}/polylog(n). This improves previously know estimate due to S.Szarek, and confirms a conjecture of A.Naor. The proof is based on probabilistic arguments.