MIT-Harvard-MSR Combinatorics Seminar: New quantitative Helly-type theorems for diameter


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May 4, 2022 4:15 pm - 5:15 pm
MIT, Room 2-139

Travis Dillon - MIT

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.