Algebra Seminar: Easdown -- Presentations of maximal subgroups of semigroups generated by idempotents subject to relations that come from the underlying biordered set

The last Algebra Seminar of 2011 will be given on Friday 16 December, by David Easdown.
Note the unusual room.  

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Speaker: David Easdown (University of Sydney) 

Date: Friday 16 December 

Time: 12:05-12:55pm 

Venue: Carslaw 375 

Title: 

Presentations of maximal subgroups of semigroups generated by idempotents subject to
relations that come from the underlying biordered set 

Abstract: 

We discuss a geometric construction, using fundamental groups of graphs, to produce
presentations of maximal subgroups of semigroups generated by elements of a biordered
set, subject to relations associated with basic products.  We relate this to recent
combinatorial results of Gray and Ruskuc (2011) that show, in particular, that the
semigroup presentation has unsolvable word problem.  We introduce the original notion of
biorder due to Nambooripad (1975) and Easdown’s arrow diagrams (1985), illustrate the
notion of singular squares in a biordered set, and how they lead to geometric
interpretations that explain interesting phenomena involving recent break-through
examples of Dolinka (2011), Brittenham, Margolis and Meakin (2009).  This is joint work
with Brett McElwee.
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Anne Thomas - anne.thomas@sydney.edu.au
Seminar website - http://www.maths.usyd.edu.au/u/AlgebraSeminar/