 CARMA COLLOQUIUM
 Speaker: ARC Laureate Fellow George Willis, CARMA, The University of Newcastle
 Title: Functions on groups
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 11^{th} Sep 2014
 Abstract:
The topological and measure structures carried by locally compact groups make them precisely the class of groups to which the methods of harmonic analysis extend. These methods involve study of spaces of real or complexvalued functions on the group and general theorems from topology guarantee that these spaces are sufficiently large. When analysing particular groups however, particular functions deriving from the structure of the group are at hand. The identity function in the cases of $(\mathbb{R},+)$ and $(\mathbb{Z},+)$ are the most obvious examples, and coordinate functions on matrix groups and growth functions on finitely generated discrete groups are only slightly less obvious.
In the case of totally disconnected groups, compact open subgroups are essential structural features that give rise to positive integervalued functions on the group. The set of values of $p$ for which the reciprocals of these functions belong to $L^p$ is related to the structure of the group and, when they do, the $L^p$norm is a type of $\zeta$function of $p$. This is joint work with Thomas Weigel of Milan.
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