Morning talks will take place in Goldsmith 226.
Afternoon talks will be in Goldsmith 317.
Schedule--Friday, April 24
| 10:00-10:30 AM | Coffee and registration | |
| 10:30-11:30 AM | Ralph Bremigan | Quotients by Complex, Compact, and Real Groups |
| 11:45-12:45 PM | David Wehlau | A Survey of Separating Invariants |
| 1:00-2:30 PM | Lunch | |
| 2:30-3:30 PM | Loek Helminck | Orbit decompositions in symmetric spaces |
| 3:30-4:00 PM | Tea | |
| 4:00-5:00 PM | Jerzy Weyman | Quivers, Clusters, Pictures |
| 6:00-9:00 PM | Banquet |
Abstracts
Ralph Bremigan: Quotients by Complex, Compact, and Real Groups
For several decades, moment map techniques have been used to study group actions, in such settings as linear actions of complex reductive groups on vector spaces and projective spaces, complex group actions on Stein and compact Kaehler manifolds, and generalizations to real group actions. We will give an overview, highlighting work of Gerry Schwarz, and discussing some new examples.
Loek Helminck: Orbit decompositions in symmetric spaces
Orbit decompositions play a fundamental role in the study of symmetric k-varieties and their applications to representation theory and many other areas of mathematics, such as geometry, the study of automorphic forms and character sheaves. Symmetric k-varieties generalize symmetric varieties and real symmetric spaces and are defined as the homogenous spaces Gk/Hk, where G is a connected reductive algebraic group defined over a field k of characteristic not 2, H the fixed point group of an involution σ and Gk (resp. Hk) the set of k-rational points of G (resp. H).
In this talk we give a survey of results on the various orbit decompositions which are of importance in the study of these symmetric k-varieties and their applications with an emphasis on orbits of parabolic and symmetric k-subgroups acting on symmetric k-varieties. We will illustrate the main results with examples and also discuss some open problems.
David Wehlau: A Survey of Separating Invariants
One of the original goals of classical invariant theory is to attempt to distinguish different group orbits by means of invariant functions. In this talk we consider separating subalgebras $S$ of an invariant ring. A subalgebra S is said to be separating if whenever any two points can be separated by any invariant, then they can also be separated by an invariant from S. Clearly the full ring of invariants is always separating. But it turns out that in many cases there are proper subalgebras which are also separating. Furthermore often there exist separating subalgebras which are more well-behaved than is the ring of invariants. I will survey what is known about separating subalgebras and explain some important open questions.
Jerzy Weyman: Quivers, Clusters, Pictures
In this talk I will describe certain combinatorial structure of generalized associahedra appearing in several apparently unrelated constructions. The combinatorics of general decompositions of quiver representations turns out to be closely related to the theory of cluster algebras of Fomin-Zelevinsky and to the Igusa-Orr theory of pictures designed to describe the homology of nilpotent groups of upper-triangular matrices.
Departing from the definition of quiver representations and Gabriel theorem I will define the generalized associahedra and sketch how they appear in the other areas mentioned above.