Organizers: Lior Gishboliner and Sepehr Hajebi.
About: This is a combinatorics seminar with little to no pressure from the clock: talks can comfortably run for up to 90 minutes (and sometimes even longer).
Format: Talks are held on Zoom and will be recorded and posted online.
Schedule: The seminar will run in rounds of 8-10 talks, for as long as speakers and audiences can be found. The schedule for Round 1 is below.
Mailing list: Announcements and Zoom information for the talks are sent to the seminar’s mailing list. To join the list, please email this address.
Round 1 (2026)
Tuesdays at 10:00 a.m. ET, October 6 to December 1 (except October 27).
October 6
October 13
Speaker: Benny Sudakov (ETH Zürich)
Title: The Mihail-Vazirani conjecture and strong edge-expansion in random 0/1 polytopes
Abstract
We study the edge-expansion of the graph of a random \(0/1\) polytope \(P^d_p\), the convex hull of a random subset of \(\{0,1\}^d\) obtained by retaining each point independently with probability \(p\). This problem, introduced by Gillmann and Kaibel more than twenty years ago, has since attracted substantial attention. We prove that, for every fixed \(\varepsilon>0\) and every \(p\in(0,1-\varepsilon]\), the graph of \(P^d_p\) has edge-expansion \(\Theta(d)\) with high probability, improving the previous best bound of Ferber, Krivelevich, Sales and Samotij and verifying the Mihail--Vazirani conjecture for random \(0/1\) polytopes in a strong form. We further show that the behavior changes sharply at \(p=1/2\): for every fixed \(\varepsilon>0\) and integer \(k\ge 2\), if \(p\le 1/2-\varepsilon\), then the edge-expansion is \(\Omega(d^k)\) with high probability. Thus, random \(0/1\) polytopes exhibit a striking expansion phase transition at \(p=1/2\). This is joint work with Micha Christoph, Sahar Diskin, Lyuben Lichev.
Recording
TBA October 20
November 3
November 10
Speaker: Sophie Spirkl (University of Waterloo)
Title: Cliques and coloring in tournaments
Abstract
Tournaments are orientations of complete graphs, and many graph theory questions -- in particular, from the world of induced subgraphs -- have analogues in tournaments. In particular, notions of colouring (due to Neumann-Lara) and clique number (Aboulker, Aubian, Charbit, Lopes) exist. I will tell you what these are, as well as some of what we know about them, and questions that remain.
Recording
TBA November 17
November 24
December 1