ICTS:29113

Video URL

Coxeter groups are biautomatic - 3

Coxeter groups are biautomatic - 3

(2024). Coxeter groups are biautomatic - 3. SciVideos. https://youtube.com/live/g7pXcWTcXF0

Coxeter groups are biautomatic - 3. SciVideos, Aug. 01, 2024, https://youtube.com/live/g7pXcWTcXF0 

          @misc{ scivideos_ICTS:29113,
            doi = {},
            url = {https://youtube.com/live/g7pXcWTcXF0},
            author = {},
            keywords = {},
            language = {en},
            title = {Coxeter groups are biautomatic - 3},
            publisher = {},
            year = {2024},
            month = {aug},
            note = {ICTS:29113 see, \url{https://scivideos.org/icts-tifr/29113}}
          }
Piotr Przytycki (McGill, Canada) & Damian Osajda (UCPH, Denmark)
Talk numberICTS:29113
Source RepositoryICTS-TIFR
Source EventGeometry in Groups
Collection

Abstract

In 1993 Brink and Howlett proved that the Davis-Shapiro (regular) language provides an automatic structure for Coxeter groups. This means that appropriate paths in the Cayley graph fellow travel, and allows to effectively solve the Word Problem. Similarly, having a bi-automatic structure allows to solve the Conjugacy Problem. However, the Davis-Shapiro language fails to be bi-automatic, even though the Conjugacy Problem for Coxeter groups has been solved by Krammer.

Other languages have been studied over the years, but only recently we came across one (that we call ‘voracious’) giving the bi-automaticity of Coxeter groups. In this minicourse we will explain the proof of our theorem. It involves the Parallel Wall Theorem of Brink and Howlett, the CAT(0) geometry of the Davis complex, and the bipodality of Dyer and Hohlweg.

Pre-requisites: Before the minicourse, please read Sections 1.1, 2.1, and 2.2 of the book ‘Lectures on buildings’ by Ronan.