Group Actions, Dynamics and Geometry Seminar

Brown Math Dept. Kassar 105
Thursdays (mostly bi-weekly) at 4-5pm

Current Schedule (2012 Fall)

• Oct 4: Zhenqi Wang (Yale University)
  
  Title: Cocycle rigidity of parabolic actions in SL(n, R), n >3.
  
  Abstract: For traditional horocycle flow in SL(2, R), the detailed analysis of the cohomological equation Uf=g was given by Flaminio-Forni. Their result was further applied in some rank-one models to obtaine cocycle rigidity for higher rank parobolic actions. In this talk I will discuss a general result about cocycle rigidity of parabolic actions and will show how to use representation tool in higher rank Lie groups.
  
  
• Oct 18: David Constantine (Wesleyan University)
  
  Title: Group actions and compact Clifford-Klein forms of homogeneous spaces.
  
  Abstract: A compact Clifford-Klein form of the homogeneous space J\H is a compact manifold J\H/\Gamma constructed using a discrete subgroup \Gamma of H. I will briefly survey the existence problem for compact forms, and will show how the existence of an action by a large (higher-rank) semisimple group proves that many spaces do not have compact forms. I will also make some remarks on a conjecture of Kobayashi on the scarcity of compact forms.
  
  
• Nov 8: Jayadev Athreya (University of Illinois Urbana-Champaign)
  
  Title: Logarithm laws for strong unstable foliations in negative curvature.
  
  Abstract: Given a finite volume negatively curved Riemannian manifold M, we give a precise relation between the logarithmic growth rates of the excursions into cusps neighborhoods of the strong unstable leaves of negatively recurrent unit vectors of M and their linear divergence rates under the geodesic flow.
  
  
• Nov 15: Ralf Spatzier (University of Michigan)
  
  Title: Global rigidity of higher rank abelian Anosov actions
  
  Abstract: This talk concerns smooth global rigidity of Anosov actions, and in particular a recent result by Fisher, Kalinin and myself. I will discuss the ideas and ingredients in its proof. In particular, this involves recent results on exponential mixing of automorphisms of nilmanifolds by Gorodnik and myself.