Definable Perfect Matchings by Prof. Jenna Zomback, Williams College, Mathematics Faculty Seminar
Fri, March 10th, 2023
1:00 pm - 1:45 pm
- This event has passed.
Definable Perfect Matchings by Prof. Jenna Zomback, Williams College, Mathematics Faculty Seminar, Friday, March 10, 1 – 1:45 pm, North Science Building 015, Wachenheim.
Abstract: In graph theory, a perfect matching in a graph is a subset M of the edges such that each vertex is adjacent to exactly one edge in M. We are often interested in when perfect matchings exist, and how we might go about constructing them (for example, matching medical students to residency programs).
In this talk, we will investigate when “definable” perfect matchings exist in infinite graphs. Kőnig proved that every d-regular bipartite graph has a perfect matching, but the resulting matching is often not definable. Our main result is that every d-regular one-ended bipartite Borel graph admits a Borel perfect matching generically. This talk is based on joint work with Matt Bowen and Antoine Poulin.