"Gelfand pairs and invariant distributions"
by
Dmitry Gourevitch
(Institute for Advanced Studies, USA)

Abstract:

First I will introduce the notion of Gelfand pair and its connection to 
invariant functions and distributions on the group, and give some 
examples. We will start from finite groups and compact groups and then 
go on to reductive groups over local fields (for example, GL(n,R) or 
GL(n,Q_p) ).
Then we will list some recent results on Gelfand pairs.
At the end we will discuss some tools used to achieve those results, and 
demonstrate them on the concrete example of the pair (GL(2,F), GL(1,F)).