SMS scnews item created by Alex Casella at Mon 16 Oct 2017 1052
Type: Seminar
Distribution: World
Expiry: 15 Jan 2018
Calendar1: 23 Oct 2017 1700-1800
CalLoc1: Carslaw 535A
CalTitle1: MaPSS: Mathematical Postgraduate Seminar Series
Auth: casella@10.17.27.71 (acas5565) in SMS-WASM

# MaPSS: Mathematical Postgraduate Seminar Series: Yee Yau (Sydney University) -- Finite State Automata for Coxeter Groups

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.