| Speaker: | Andy Zucker |
| Affiliation: | University of Waterloo |
| Location: | MC 5501 |
Abstract: Ramsey's celebrated theorem has two forms — an infinite version and a finite one. A natural way to try to generalize the theorem is to color substructures of a given structure, rather than just subsets of a given set. A 1977 theorem of Nesetril and Rodl provides a sweeping generalization of the finite version of Ramsey's theorem to all relational free-amalgamation classes of finite structures. For the infinite version, things get much more complicated. While a 2022 theorem of mine proves a generalization of the infinite version for finitely-constrained binary free-amalgamation classes, the result in full generality is false dropping either the finite-constraint assumption or the binary assumption. Time permitting, I will discuss joint work with Joey Lakerdas-Gayle discussing some of the strange things that can happen for infinitely-constrained binary free-amalgamation classes.