Type: Seminar

Distribution: World

Expiry: 15 Jan 2018

CalTitle1: MaPSS: Mathematical Postgraduate Seminar Series

Auth: casella@10.17.27.71 (acas5565) in SMS-WASM

Dear All, We are delighted to present the MaPSS Seminar topic of Monday 16/10; please see the abstract below. **This Semester the Seminar will always run on Monday, at 5:00pm in 535A** Following the talk, there will be pizza on offer. Speaker: Yee Yau (Sydney University) Title: Finite State Automata for Coxeter Groups Abstract: Coxeter groups are abstract reflection groups with a straightforward group presentation consisting of generators and relations. Whilst the presentation is economical, it gives notoriously little information about the nature of its elements. For example, given an arbitrary string of generators, is it possible to know whether the expression is "reduced"? In 1993, members of the University of Sydney’s School of Mathematics and Statistics, Brigitte Brink and A. Prof. Bob Howlett produced seminal work in the area of Coxeter groups which precisely answered the above question. They proved: "For every Coxeter group, there exists a finite state automaton which recognises the language of reduced words". Informally, in this context, a finite state automaton is a "machineâ€ capable of "reading" words in the generators and giving an answer of "Yes" if and only if the group element represented by the word cannot be expressed with a shorter string of generators. The aim of this talk is to give a brief introduction to Coxeter groups and describe how we can build a finite state automaton to study Coxeter groups by following the work of Brink and Howlett. Supervisors, please encourage your students to attend. Thanks, MaPSS Organizers