Rankin-Selberg integrals provide factorization of certain period
integrals into local counterparts. Other, more elusive, periods can
be studied in principle by the relative trace formula and other
methods.
I will discuss Knop's paper generalizing Harish-Chandra's
isomorphism for the center of the universal enveloping algebra to
the setting of spherical varieties. Here the center is replaced by
the algebra of invariant differential operators. The idea...
Rankin-Selberg integrals provide factorization of certain period
integrals into local counterparts. Other, more elusive, periods can
be studied in principle by the relative trace formula and other
methods.
I will explain an application of the geometric Satake
correspondence (in its derived form due to
Bezrukavnikov-Finkelberg) to the study of differential operators on
$G$-spaces (for $G$ complex reductive) and its classical version,
the study of...
We will discuss Knop's paper "The asymptotic behavior of
invariant collective motion" which analyzes the moment map for a
spherical variety and relates it to a Weyl group.
In these lectures, we will explore what insight can be gained
into the arithmetic of Galois representations in a given dimension
through the geometry of a higher-dimensional locally symmetric
space near a boundary component. The starting point for...
I will give a brief introduction to spherical varieties. With a
view towards understanding the geometry of the moment map, I'll
talk about the local structure theorem for spherical varieties.
More concretely, if X is a spherical G-variety and B a...
