MATH Seminar

Title: On Pisier type problems
Defense: Dissertation
Speaker: Marcelo Sales of Emory University
Contact: Marcelo Sales,
Date: 2023-04-05 at 4:00PM
Venue: MSC N301
Download Flyer
A subset $A$ of integers is \textit{free} if for every two distinct subsets $B, B'\subset A$ we have \[\sum_{b\in B}b\neq \sum_{b'\in B'} b'.\] Pisier asked if, for every subset $A$ of integers, the following two statements are equivalent:\\ \\ (1) $A$ is a union of finitely many free sets.\\ (2) There exists $\epsilon>0$ such that every finite subset $B\subset A$ contains a free subset $C\subset B$ with $|C|\geq \epsilon |B|$.\\ \\ In a more general framework, the Pisier question can be seen as the problem of determining if statements (1) and (2) are equivalent for subsets of a given structure with the prescribed property. We study the problem for several structures including $B_h$-sets, arithmetic progressions, independent sets in hypergraphs, and configurations in the euclidean space.

See All Seminars