Geometry & Topology Seminar

Geometry & Topology Seminar 

Date: Wednesday, 9 September 2026 

Time: 12noon-1pm 

Speaker: Fabricio Dos Santos (The University of Sydney) 

Location: SMRI Seminar Room (Macleay A12 Room 301) 

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 explain how to 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.