Type: Seminar

Distribution: World

Expiry: 5 Sep 2016

CalTitle1: Groups Actions Seminar, Dooley

Calendar2: 5 Sep 2016 1500-1600

CalLoc2: Carslaw 175

CalTitle2: Group Actions Seminar, Ferov

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

The next Group Actions Seminar will be on Monday 5 September at the University of Sydney. The schedule, titles and abstracts are below. -------------------------------------------------------------------------- 12 noon-1pm, Carslaw 350 Speaker: Anthony Dooley, University of Technology Sydney Title: The Kirillov orbit method, wrapping maps and $e$-functions Abstract: Kirillov’s character formula gives an expression for the character of an irreducible representation of a Lie group in terms of the (Euclidean) Fourier transform of its associated coadjoint orbit. Wildberger and I re-interpreted this using the wrapping map, which allows one to transfer Ad-invariant distributions from the Lie algebra to the Lie group, as a convolution homomorphism. In this talk, I will describe how the theory works for compact symmetric pairs (G,K). The convolution of $K$-invariant distributions needs to be twisted by the so-called $e$-function, and one then retrieves the characters of $G/K$ as limits of generalised Bessel functions. 1-3pm Lunch 3-4pm, Carslaw 175 Speaker: Michal Ferov, The University of Newcastle Title: Amenable quotients of graph products of groups Abstract: A group is amenable if it admits a left-invariant Haar measure (there are many different equivalent definitions). It is well known fact that not all groups are amenable, the easiest example being the free group. One can then ask: if group G is not amenable, can we at least homomorphically map every non-trivial element of G onto a non-trivial element of an amenable group, i.e. does every non-trivial element of G survive in some amenable quotient of G? Groups with this property are called residually amenable. In the talk I will introduce the graph product of groups, group-theoretic construction naturally generalising the concept of direct and free product in the category of groups, and show that the class of residually amenable groups is closed under forming graph products. This talk is based on the paper (http://arxiv.org/abs/1505.05001) co-authored with F. Berlai. -------------------------------------------------------------------------