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<font face="Tahoma" size="2"><b>From:</b> noreply+automations@airtableemail.com <noreply+automations@airtableemail.com>On Behalf OfTheoryBot (via Airtable) <noreply+automations@airtableemail.com><br>
<b>Sent:</b> Wednesday, May 17, 2023 12:51:20 AM (UTC-06:00) Central Time (US & Canada)<br>
<b>To:</b> Antares Chen <antaresc@uchicago.edu><br>
<b>Cc:</b> Christopher Kang <ctkang@uchicago.edu><br>
<b>Subject:</b> Theory Lunch 2023-05-17T17:30:00.000Z<br>
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<p style="margin-top:0"><span>Today's Theory Lunch talk:</span></p>
<p><em><span>Alex Hoover (University of Chicago): Surprising power from information theory: the union-closed conjecture</span></em></p>
<p><span><a href="https://urldefense.com/v3/__https://uchicago.zoom.us/j/91616319229?pwd=dDdXQnFXeGNubFRkZy9hTDQrcWlXdz09__;!!BpyFHLRN4TMTrA!98439WXDZNFvb975VmZo0Yo3tcFLuuk5pUsBU1OG9-BpMnuvdW0M0OjIGpGZ2p4PTk0t6O3hmEo9VCtZmqQnCxuu4pBfJzKAe8E$">https://uchicago.zoom.us/j/91616319229?pwd=dDdXQnFXeGNubFRkZy9hTDQrcWlXdz09</a></span></p>
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<p><span>Description: In 1979, Peter Frankl conjectured that in any union-closed set-family, there would be an element present in at least half of the sets in the family. Over the next 40 years, there were quite a few publications making progress toward proving
this conjecture, considering special casses or reformulations of the problem. And, late last year, Justin Gilmer posted a breakthrough paper where he improved the bound on the number of sets some element must be in, from inverse-logarithmic to constant. Since
his work, the constant has been improved to the limits of the technique he used. In this talk, I’ll explain the union-closed conjecture and go over the simple information-theoretic tools and techniques used by Gilmer to establish his result.</span></p>
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<p><span>Relevant paper: <a href="https://urldefense.com/v3/__https://arxiv.org/abs/2211.09055__;!!BpyFHLRN4TMTrA!98439WXDZNFvb975VmZo0Yo3tcFLuuk5pUsBU1OG9-BpMnuvdW0M0OjIGpGZ2p4PTk0t6O3hmEo9VCtZmqQnCxuu4pBf5SSbrMw$">
https://arxiv.org/abs/2211.09055</a></span></p>
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<div>©2023 Airtable</div>
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