Online talk: Meike Hatzel

Monday, February 1, 3pm ET (8pm GMT, 9am Tue NZDT)
Meike Hatzel, TU Berlin
Perfect Matching Width and a grid minor theorem for bipartite graphs


The grid theorem stating that a graph has small treewidth if and only if it contains no large grid as a minor is known to be an important step in the work by Robertson and Seymour leading to the graph structure theorem. Norine conjectured that a similar property holds on graphs in which every edge is contained in a perfect matching for a bipartite grid version and a width parameter called Perfect matching width. This talk presents a partial solution to this conjecture. We prove a grid theorem using perfect matching width on bipartite graphs by showing that it is equivalent to the directed treewidth and thus we can transfer the directed grid theorem by Kawarabayashi and Kreutzer.

Online talk: ‪Liana Yepremyan‬

Monday, January 25, 3pm ET (8pm GMT, 9am Tue NZDT)
‪Liana Yepremyan‬, LSE and UIC
Ryser’s conjecture and more

Password: email rose.mccarty ~at~ uwaterloo ~.~ ca if you need the password

A Latin square of order $n$ is an $n \times n$ array filled with $n$ symbols such that each symbol appears only once in every row or column and a transversal is a collection of cells which do not share the same row, column or symbol. The study of Latin squares goes back more than 200 years to the work of Euler. One of the most famous open problems in this area is a conjecture of Ryser, Brualdi and Stein from 60s which says that every Latin square of order $n\times n$ contains a transversal of order $n-1$. A closely related problem is 40 year old conjecture of Brouwer that every Steiner triple system of order $n$ contains a matching of size $(n-4)/3$. The third problem we’d like to mention asks how many distinct symbols in Latin arrays suffice to guarantee a full transversal? In this talk we discuss a novel approach to attack these problems.

Joint work with Peter Keevash, Alexey Pokrovskiy and Benny Sudakov.

Online talk: Kazuhiro Nomoto

Monday, January 18, 3pm ET (8pm GMT, 9am Tue NZDT)
Kazuhiro Nomoto, University of Waterloo
$I_t$-free, triangle-free binary matroids


For any integer $t \geq 1$, we say that a simple binary matroid is $I_t$-free if no rank-$t$ flats are independent. It is triangle-free if it has no circuit of size $3$. In this talk, we discuss a few problems regarding simple $I_t$-free, triangle-free binary matroids, with some partial results.

Joint work with Peter Nelson.

A list of blog content in 2021

As things can get hard to find on the blog, I’ll be updating this post with links to our content from this year, after the fact.
For upcoming talks and a permanent link to this post, see the “Talks” page.

Past online talks:

Blog Posts