MIT-Harvard-MSR Combinatorics Seminar

Wednesday, May 04, 2022 at 4:15pm to 5:15pm

MIT - Dept. of Mathematics, Bldg. 2, Room 139

Speaker;  Travis Dillon  (MIT)

Title:  New quantitative Helly-type theorems for diameter

Abstract

Helly's theorem is a fundamental statement in discrete and convex geometry that relates the intersection of a family of convex sets to the intersections of its subfamilies. This talk surveys recent advances in quantitative versions of Helly's theorem, including best-known results toward proving a 1982 conjecture of Bárány, Katchalski, and Pach. Along the way, I'll introduce a new, surprisingly powerful technique for proving quantitative Helly-type theorems, and we'll completely characterize the norms for which there is a ``no-loss'' Helly-type theorem for diameter.

This talk is based on joint work with Pablo Soberón.

Event Type

Conferences/Seminars/Lectures

Events By Interest

Academic

Events By Audience

MIT Community

Events By School

School of Science

Website

https://math.mit.edu/sites/combin/

Department
Department of Mathematics
Contact Email

daisymae@math.mit.edu

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