Type: Seminar

Distribution: World

Expiry: 4 May 2023

CalTitle1: SMRI Seminar: Gray ’Subgroups of inverse monoids via the geometry of their Cayley graphs’

Auth: hannahb@staff-10-48-24-167.vpnuser.sydney.edu.au (hbry8683) in SMS-SAML

SMRI Seminar ’Subgroups of inverse monoids via the geometry of their Cayley graphs’ Robert Gray (University of East Anglia) Thursday 4th May 1:00-2:00pm Quad S249 & via Zoom (register/join https://uni-sydney.zoom.us/j/82516271060) Abstract: In the 1960’s Higman was able to characterize the finitely generated subgroups of finitely presented groups, that is, groups defined using a finite set of generators and finite set of defining relations. His result, which is called the Higman Embedding Theorem, is a key result in combinatorial group theory which makes precise the connection between group presentations and logic. In this talk I will present a result of a similar flavour, proved in recent joint work with Mark Kambites (Manchester), in which we characterise the groups of units of inverse monoids defined by presentation where all the defining relators are of the form w=1. I will explain what an inverse monoid is, the motivation for studying this class of inverse monoids, and also outline some of the geometric ideas that we developed in order to prove our results. Speaker bio: Robert Gray is a Reader in Pure Mathematics and an EPSRC Research Fellow at the University of East Anglia in the UK. His research lies at the interface of algebra, logic, and theoretical computer science. A central theme in his recent research has been the study of certain fundamental algorithmic questions for infinite groups, monoids and inverse semigroups, using methods from infinite combinatorics, topology, geometry and theoretical computer science. ---- Please join us after the seminar for SMRI afternoon tea, 2:00-2:45pm every Thursday on the SMRI Terrace (accessed through A14-04-L4.36) ---- Upcoming SMRI events can be found here: https://mathematical-research-institute.sydney.edu.au/news-events/ SMRI YouTube Channel: https://www.youtube.com/c/SydneyMathematicalResearchInstituteSMRI

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