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Current Programs

  1. Dynamics on Moduli Spaces of Geometric Structures

    Organizers: Richard Canary (University of Michigan), William Goldman (University of Maryland), François Labourie (Université de Nice Sophia Antipolis), LEAD Howard Masur (University of Chicago), Anna Wienhard (Ruprecht-Karls-Universität Heidelberg)

    The program will focus on the deformation theory of geometric structures on manifolds, and the resulting geometry and dynamics. This subject is formally a subfield of differential geometry and topology, with a heavy infusion of Lie theory. Its richness stems from close relations to dynamical systems, algebraic geometry, representation theory, Lie theory, partial differential equations, number theory, and complex analysis.

    Updated on Jul 29, 2013 03:58 PM PDT
  2. Geometric and Arithmetic Aspects of Homogeneous Dynamics

    Organizers: LEAD Dmitry Kleinbock (Brandeis University), Elon Lindenstrauss (Hebrew University), Hee Oh (Yale University), Jean-François Quint (University de Bordeaux 1), Alireza Salehi Golsefidy (University of California, San Diego)

    Homogeneous dynamics is the study of asymptotic properties of the action of subgroups of Lie groups on their homogeneous spaces. This includes many classical examples of dynamical systems, such as linear Anosov diffeomorphisms of tori and geodesic flows on negatively curved manifolds. This topic is related to many branches of mathematics, in particular, number theory and geometry. Some directions to be explored in this program include: measure rigidity of multidimensional diagonal groups; effectivization, sparse equidistribution and sieving; random walks, stationary measures and stiff actions; ergodic theory of thin groups; measure classification in positive characteristic. It is a companion program to “Dynamics on moduli spaces of geometric structures”.

    Updated on Jan 12, 2015 10:58 AM PST