2018
Oct
24

# Analysis Seminar: Boaz Slomka (WIS) "An improved bound for Hadwiger’s covering problem via thin shell inequalities for the convolution square"

12:00pm to 1:00pm

## Location:

Room 70, Ross building

Title: An improved bound for Hadwiger’s covering problem via thin shell inequalities for the convolution square.

Abstract: A long-standing open problem, known as Hadwiger’s covering problem, asks what is the smallest natural number N(n) such that every convex body in {\mathbb R}^n can be covered by a union of the interiors of at most N(n) of its translates. Despite continuous efforts, the best-known general upper bound for this number remain as it was more than half a decade ago, and is of the order of \binom{2n}{n}n\ln n.

Abstract: A long-standing open problem, known as Hadwiger’s covering problem, asks what is the smallest natural number N(n) such that every convex body in {\mathbb R}^n can be covered by a union of the interiors of at most N(n) of its translates. Despite continuous efforts, the best-known general upper bound for this number remain as it was more than half a decade ago, and is of the order of \binom{2n}{n}n\ln n.