MIT-Harvard-MSR Combinatorics Seminar

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.