[Theory] FW: Theory Lunch 2023-05-17T17:30:00.000Z

[Christopher Kang]

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Sent: Wednesday, May 17, 2023 12:51:20 AM (UTC-06:00) Central Time (US & Canada)
To: Antares Chen <antaresc at uchicago.edu>
Cc: Christopher Kang <ctkang at uchicago.edu>
Subject: Theory Lunch 2023-05-17T17:30:00.000Z


Today's Theory Lunch talk:

Alex Hoover (University of Chicago): Surprising power from information theory: the union-closed conjecture

https://uchicago.zoom.us/j/91616319229?pwd=dDdXQnFXeGNubFRkZy9hTDQrcWlXdz09<https://urldefense.com/v3/__https://uchicago.zoom.us/j/91616319229?pwd=dDdXQnFXeGNubFRkZy9hTDQrcWlXdz09__;!!BpyFHLRN4TMTrA!98439WXDZNFvb975VmZo0Yo3tcFLuuk5pUsBU1OG9-BpMnuvdW0M0OjIGpGZ2p4PTk0t6O3hmEo9VCtZmqQnCxuu4pBfJzKAe8E$>

Description: In 1979, Peter Frankl conjectured that in any union-closed set-family, there would be an element present in at least half of the sets in the family. Over the next 40 years, there were quite a few publications making progress toward proving this conjecture, considering special casses or reformulations of the problem. And, late last year, Justin Gilmer posted a breakthrough paper where he improved the bound on the number of sets some element must be in, from inverse-logarithmic to constant. Since his work, the constant has been improved to the limits of the technique he used. In this talk, I’ll explain the union-closed conjecture and go over the simple information-theoretic tools and techniques used by Gilmer to establish his result.

Relevant paper: https://arxiv.org/abs/2211.09055<https://urldefense.com/v3/__https://arxiv.org/abs/2211.09055__;!!BpyFHLRN4TMTrA!98439WXDZNFvb975VmZo0Yo3tcFLuuk5pUsBU1OG9-BpMnuvdW0M0OjIGpGZ2p4PTk0t6O3hmEo9VCtZmqQnCxuu4pBf5SSbrMw$>

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