List of upcoming online seminars in discrete mathematics, combinatorics, and graph theory

Title: Recent progress in Ramsey Theory
by Jacques Verstraete (UCSD) as part of UCLA Combinatorics Forum

Lecture held in MS 6627.

Abstract
The Ramsey number $r(s,t)$ denotes the minimum $N$ such that in any red-blue coloring of the edges of the complete graph $K_N$, there exists a red $K_s$ or a blue $K_t$. While the study of these quantities goes back almost one hundred years, to early papers of Ramsey and Erdős and Szekeres, the long-standing conjecture of Erdős that $r(s,t)$ has order of magnitude close to $t^{s–1}$ as $t\to \mathrm{\infty }$ remains open in general. It took roughly sixty years before the order of magnitude of $r(3,t)$ was determined by Jeong Han Kim, who showed $r(3,t)$ has order of magnitude $t^2/(\log t)$ as $t\to \mathrm{\infty }$. In this talk, we discuss a variety of new techniques, including mention of the proof that for some constants $a,b>0$ and $t\ge 2$,
$$a\frac{t^3}{(\log t{)}^4}\le r(4,t)\le b\frac{t^3}{(\log t{)}^2},$$
as well as new progress on other Ramsey numbers, on Erdős-Rogers functions, Ramsey minimal graphs, and on coloring hypergraphs.

Joint work in part with David Conlon, Sam Mattheus, and Dhruv Mubayi.

Title: Gadgets in percolation
by Nikita Gladkov (UCLA) as part of UCLA Combinatorics Forum

Lecture held in MS 6627.

Abstract
Suppose that, due to a marathon, each street in Los Angeles has a 1/2 chance of being closed. With nothing better to do, your n friends, who live in different parts of the city, try to figure out which subgroups can still assemble. We explore the possible distributions over the set of resulting partitions based on computer experiments and discuss the known inequalities.

by Daoji Huang (IAS) as part of UCLA Combinatorics Forum

Lecture held in MS 6221.
Abstract: TBA

by Shiyue Li (IAS) as part of UCLA Combinatorics Forum

Lecture held in MS 6221.
Abstract: TBA