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

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.  

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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) 

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