Group Actions Seminar: Piggott, Naqvi

The next Group Actions Seminar will be on Tuesday 23 October at the University of
Sydney.  The schedule, titles and abstracts are below.  

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11am - Noon, Carslaw 357 

Speaker: Adam Piggott, The University of Queensland 
Title: On groups presented by length-reducing rewriting systems 

Abstract: A rewriting system comprises an alphabet and some rules for simplifying words
over the alphabet.  Each rewriting system "presents" a monoid, and sometimes that monoid
is a group.  It is natural to ask which groups admit a presentation by particularly nice
rewriting systems.  In 1984 Gilman conjectured that the groups which can be presented by
finite convergent monadic rewriting systems are exactly the plain groups.  We will
discuss a proof, discovered in collaboration with Andy Eisenberg (St Louis University),
that Gilman was right.  We will also discuss questions concerning groups presented by
length-reducing rewriting systems which remain unresolved.  

Noon - 2pm Lunch 

2-3pm, Carslaw 373 

Speaker: Yusra Naqvi, The University of Sydney 
Title: Reconstructing simplicial group actions 

Abstract: This talk will describe algorithms which compress and reconstruct finite
symmetric simplicial complexes.  These algorithms are derived from generalisations (by
Bridson-Haefliger, Carbone-Rips, and Corson, among others) of the classical Bass-Serre
theory for reconstructing group actions on trees.  The compression algorithm takes in a
finite simplicial complex along with a subgroup G of its automorphism group, and outputs
a complex of groups.  The reconstruction algorithm inverts the first by using the
overlaid algebraic data to correctly unfold the complex of groups so that the simplicial
complex is recovered up to G-equivariant isomorphism.  This talk is based on joint work
with Lisa Carbone and Vidit Nanda.