Title: Domino tilings beyond 2D
Abstract: There is a rich history of domino tilings in two dimensions. Through a variety of techniques we can answer questions such as: how many tilings are there of a given region or what does a random tiling look like? These questions and their answers become significantly more difficult in dimension three and above. Despite this curse of dimensionality, I will discuss recent advances in the theory. I will also highlight problems that still remain open.
Title: Recognizing Right-Angled Coxeter Groups
Abstract: In this talk, I will discuss joint work with Cunningham, Eisenberg, and Piggott from several years ago about how to recognize when you might be staring at a right-angled Coxeter group. In particular, if you have a group generated by finitely many involutions, each pair either commutes or generated an infinite dihedral group, and the only torsion in your group is 2-torsion, you might have a right-angled Coxeter group – but how can you possibly tell if you have one if you do not have your hands on a Coxeter presentation for that group? I will discuss why I care about this problem and I will discuss some key examples related to this question.
Wolfgang and Luise Kappe Alumni Speaker
Title: Some complicated simple groups
Abstract: Finite simple groups are, famously, classified. This is very much not the case for infinite simple groups. In this talk I will discuss some important examples of infinite simple groups, based around the (unfortunately non-descriptively-named) family of "Thompson's groups". We will move through the extended family of Thompson-like groups, eventually reaching some rather complicated and robust examples of infinite simple groups called "twisted Brin-Thompson groups" (introduced by Jim Belk and myself, following work of Matt Brin). In particular I will discuss some interesting "universality" properties of these groups in the class of infinite simple groups, following joint work of mine with Jim Belk, Francesco Fournier-Facio, and James Hyde.