Type: Seminar

Distribution: World

Expiry: 23 Oct 2018

CalTitle1: Piggott, On groups presented by length-reducing rewriting systems

Calendar2: 23 Oct 2018 1400-1500

CalLoc2: Carslaw 373

CalTitle2: Naqvi, Reconstructing simplicial group actions

Auth: timothyb@dora.maths.usyd.edu.au

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