Fabricio Dos Santos (黑料不打烊 University)

Title: Garside shadows and biautomatic structures in Coxeter groups

Abstract: In 2022, Osajda and Przytycki showed that any Coxeter group $W$ is biautomatic. Key to their proof is the notion of voracious projection of an element $g \in W$, which is used iteratively to construct a biautomatic structure for $W$: the voracious language. In this talk, I will generalize these two notions by defining them for any Garside shadow $B$ in a Coxeter system $(W,S)$. This leads to the result that any finite Garside shadow in $(W,S)$ can be used to construct a biautomatic structure for $W$. In particular, for the Garside shadow $L$ of low elements, the biautomatic structure obtained corresponds to the original voracious language of Osajda and Przytycki. These results answer a question of Hohlweg and Parkinson.

We will gather for teatime in the lounge at 4pm after the talk.