ACO Seminar - Quentin Dubroff September 19, 2024 3:00pm — 4:00pm Location: In Person - Wean Hall 8220 Speaker: QUENTIN DUBROFF, Postdoctoral Associate, Department of Mathematical Sciences, Carnegie Mellon University https://sites.google.com/view/quentin-c-dubroff/ Thresholds for graph containment in G_{n,p} and coupon collectors The first goal of this talk is to describe some recent progress (in joint work with Jeff Kahn and Jinyoung Park) on the "Second" Kahn-Kalai Conjecture (KKC2), the original conjecture on graph containment in Gn,p that motivated what is now the Park-Pham Theorem (PPT). KKC2 says that pc (H), the threshold for containing a graph H in Gn,p, satisfies pc (H) = O(pE log n), where pE is the smallest p such that the expected number of copies of any subgraph of H is at least one. In other words, for this class of problems, the expectation threshold q in PPT can be replaced by the smaller pE. We show that q < O(pE log2 n) (implying pc(H) = O(pE log3 n) via PPT). Time-permitting, the second portion of the talk will discuss some hopes for and failed attempts at sharpening PPT and KKC2. 4:00 pm → Tea and Cookies, Wean 6220 (bring your own mug if you have one). Event Website: https://aco.math.cmu.edu/abs-24-25/sep19.html
