Group Actions Seminar

Brown Math Dept. Kassar 105
Roughly every other Thursday at 4-5pm

Contact: Hee Oh

Current Schedule (Spring, 2008)

• 2/28 Nir Avni, Hebrew University/UCLA
  
  Title: Representation Growth of Groups.
  
  Abstract: For a group G, let a_n(G) be the number of n-dimensional representations of G. For certain kinds of groups (SL(n,Z) for example), the behavior of a_n(G) can be encoded in a zeta-like function. I will describe several results and open questions regarding the poles (which give the rate of growth of a_n(G)), meromorphic continuation (which gives the error terms), and functional equation (which give surprising symmetries between the a_n(G)'s) of this zeta function.
  
  
• 3/13 Danijela Damjanovic, Harvard
  Abelian actions and rigidity
  
  Abstract: I will give an overview of recent results and of some problems concerning various rigidity properties of algebraic abelian actions.
  
  
• 4/3 Gopal Prasad, U of Michigan
  Lengths of closed geodesics and isospectral locally symmetric spaces
  
  Abstract: I will give an exposition of my recent work with Andrei Rapinchuk in which we have introduced a new notion of "weak commensurability" of Zariski-dense subgroups. We have studied weak commensurability of arithmetic subgroups of semi-simple Lie groups. The notion of weak commensurability turns out to be intimately related to the commensurability of the set of lengths of closed geodesics on, and isospectrality of, locally symmetric spaces of finite volume (and with nonpositive sectional curvatures). We are in this way able to answer Marc Kac's famous question "Can one hear the shape of a drum?" for compact arithmetic locally symmetric spaces.
  
  
• 4/24 Francois Maucourant, Rennes 1 University
  Two examples of nonhomogeneous orbit closures.
  
  Abstract: We will explain how to construct orbits of non-homogeneous closure for some subgroup of the diagonal group acting on the space of lattices of dimension at least 6. Also, a similar example for the action of *2,*3 on the four dimensionnal torus is discussed.
  
  
• 5/1 Lisa Carbone, Rutgers University
  Tits buildings for hyperbolic Kac-Moody groups
  
  Abstract: We outline how to associate a simplicial complex X to the BN-pair data for a Kac-Moody group G. When G is of hyperbolic type, X is a hyperbolic building whose local structure is determined by the proper connected subdiagrams of the Dynkin diagram for G. For Kac-Moody groups over finite fields, we indicate how the action of G on X may be used to give structure theorems, generators and relations for G and its subgroups. When G is hyperbolic of rank 2 or 3 we show that G acts on a homogeneous or bihomogeneous tree.
  
  Fall 07 Schedule
  

Background poster is kindly provided by Rich Schwartz