<html><head><meta http-equiv="content-type" content="text/html; charset=utf-8"></head><body dir="auto"><span style="-webkit-text-size-adjust: auto;">Departments of Mathematics & Computer Science</span><br style="-webkit-text-size-adjust: auto;"><span style="-webkit-text-size-adjust: auto;">Combinatorics & Theory Seminar</span><br style="-webkit-text-size-adjust: auto;"><span style="-webkit-text-size-adjust: auto;"></span><br style="-webkit-text-size-adjust: auto;"><span style="-webkit-text-size-adjust: auto;">Tuesday, March 29, 3:30pm</span><br style="-webkit-text-size-adjust: auto;"><span style="-webkit-text-size-adjust: auto;"><b>Location TBA</b></span><br style="-webkit-text-size-adjust: auto;"><span style="-webkit-text-size-adjust: auto;"></span><br style="-webkit-text-size-adjust: auto;"><span style="-webkit-text-size-adjust: auto;">Yufei Zhao (MIT)</span><br style="-webkit-text-size-adjust: auto;"><span style="-webkit-text-size-adjust: auto;"></span><br style="-webkit-text-size-adjust: auto;"><span style="-webkit-text-size-adjust: auto;">TITLE: </span>Enumerating k-SAT functions<br style="-webkit-text-size-adjust: auto;"><span style="-webkit-text-size-adjust: auto;"></span><br style="-webkit-text-size-adjust: auto;"><span style="-webkit-text-size-adjust: auto;">ABSTRACT: </span>How many k-SAT functions on n boolean variables are there? What does a typical such function look like?<div><br></div><div>Bollobás, Brightwell, and Leader conjectured that for each fixed k, almost every k-SAT function is unate.</div><div><br></div><div>In this talk, I will discuss progress towards this conjecture and explain how the hypergraph container method can be used to reduce the problem to a hypergraph Turán-like problem, which is solved for k ≤ 4 but remains open in general.</div><div><br></div><div>Joint work with Dingding Dong and Nitya Mani.</div><span style="-webkit-text-size-adjust: auto;"></span><br style="-webkit-text-size-adjust: auto;"><span style="-webkit-text-size-adjust: auto;">%%%%%%%%%%%%%%%%%%%%%%%</span><br style="-webkit-text-size-adjust: auto;"><span style="-webkit-text-size-adjust: auto;">While the University no longer requires wearing masks, we will set aside a couple of tables </span><span style="-webkit-text-size-adjust: auto;">designated "masks required".</span><div><span style="-webkit-text-size-adjust: auto;">%%%%%%%%%%%%%%%%%%%%%%%</span></div><div><span style="-webkit-text-size-adjust: auto;"><br></span></div><div><span style="-webkit-text-size-adjust: auto;">Yufei will </span><span style="-webkit-text-size-adjust: auto;">give another talk at the Math Colloquium on March 30, see</span></div><div><span style="-webkit-text-size-adjust: auto;"><br></span></div><div><a href="https://mathematics.uchicago.edu/events/event/1471/">https://mathematics.uchicago.edu/events/event/1471/</a></div><div><br></div><div>for details. </div><div><div><span style="-webkit-text-size-adjust: auto;"><br></span></div><div><span style="-webkit-text-size-adjust: auto;"><br></span></div></div></body></html>