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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, February 1, 2023 12:49:46 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 2023-02-01T18:30:00.000Z<br>
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<p style="margin-top:0"><span>Today's Theory Lunch talk:</span></p>
<p><em><span>Aaron Potechin (UChicago): Sum of Squares Lower Bounds for Densest k-Subgraph</span></em></p>
<p><span><a href="https://urldefense.com/v3/__https://uchicago.zoom.us/j/91616319229?pwd=dDdXQnFXeGNubFRkZy9hTDQrcWlXdz09__;!!BpyFHLRN4TMTrA!50ueZxDp8tKkonSObHOvQFOvzZcgCbiuwi1AkFsuphr2HgJBuKGnM07FUcWKrEHklO3of3ct8Ozq0TnqXfqlTbD7sE5BS2bgCJE$">https://uchicago.zoom.us/j/91616319229?pwd=dDdXQnFXeGNubFRkZy9hTDQrcWlXdz09</a></span></p>
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<p><span>Description: In the densest k-subgraph problem, we are given a graph G and we are asked to find the subgraph of G with k vertices which has the maximum number of edges. Despite decades of research, the hardness of densest k-subgraph is only partially
understood, both in the worst case and average case settings.</span></p>
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<p><span>In this talk, I will consider the following average case variant of the densest k-subgraph problem. Can we distinguish between the following two distributions of graphs?</span></p>
<p><span>1. Random distribution: G(n,p) where p = n-𝛽.</span></p>
<p><span>2. Planted distribution: G(n,p) + G(k,q) where k = nαand q = n-𝛾.</span></p>
<p><span>I will describe the known upper bounds on this problem from the log-density framework and spectral algorithms. I will then describe our sum of squares lower bounds and how they compare to these upper bounds.</span></p>
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<div>©2023 Airtable</div>
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