Infinite Groups Seminar: East, Dani

The next Infinite Groups Seminar will be on Monday 6 June at the University of Sydney
and over the Access Grid.  The speakers will be James East at 12 noon and Pallavi Dani
at 2.30pm.  

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12:00, Access Grid Room, Carslaw 829 

Speaker: James East (University of Western Sydney) 

Title: Idempotent generators in partition monoids 

Abstract: Partition monoids and algebras arise in representation theory in the context
of Schur-Weyl duality in symmetric groups.  They are also interesting from a semigroup
theoretic point of view as they contain the full transformation semigroups as well as
the symmetric (and dual symmetric) inverse monoids.  We characterise the elements of the
partition monoid which are products of idempotent partitions.  The finite and infinite
cases require separate treatment.  Our results are similar in character to those
obtained by Howie in his 1966 paper on full transformation semigroups; in fact, Howie’s
results may also be deduced from ours.  This is joint work with Des FitzGerald.  

14:30pm, Access Grid Room, Carslaw 829 

Speaker: Pallavi Dani (Louisiana State University) 

Title: Higher Dehn functions of Bestvina-Brady groups 

Abstract: The k-dimensional Dehn function of a group captures the difficulty of filling
k-spheres by (k+1)-balls in a complex that models the group.  I will talk about a method
for modifying fillings of spheres in the complex associated with a right-angled Artin
group.  This can be used to obtain sharp bounds on the higher Dehn functions of certain
subgroups called Bestvina-Brady groups.  Similar ideas lead to estimates on higher
divergence functions in right-angled Artin groups.  This is joint work with Aaron
Abrams, Noel Brady, Moon Duchin, and Robert Young.  

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