MATH Seminar
| Title: On Pisier type problems |
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| Defense: Dissertation |
| Speaker: Marcelo Sales of Emory University |
| Contact: Marcelo Sales, marcelo.tadeu.sales@emory.edu |
| Date: 2023-04-05 at 4:00PM |
| Venue: MSC N301 |
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| Abstract: 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. |
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