Joint IAS/PU Groups and Dynamics Seminar

Motivated by the study of billiards in polyhedra, we study linear flows in a family of singular flat 3-manifolds which we call translation prisms. Using ideas of Furstenberg, and Veech, we connect results about weak mixing properties of flows on...

The theory of hierarchically hyperbolic groups, due to Behrstock, Hagen, and Sisto, was developed by abstracting work of Masur and Minsky on mapping class groups. Study of the large scale geometry of the outer automorphism group Out(Fn)

of a rank n...

Thurston gave an explicit construction of pseudo-Anosov elements

in the mapping class group of a compact surface, using Dehn twists in pairs of filling multicurves.  We show that the probability that a random walk of length n on the mapping class...

Consider a closed surface M of genus greater than or equal to 2. For negatively curved metrics on M and their corresponding geodesic flow, we can study the topological entropy, the Liouville entropy, and the mean root curvature. In 2004, Manning...

Fibered 3-manifolds are those constructed via surface homeomorphisms. Given such a manifold with pseudo-Anosov monodromy, much is already known about how topological data of the mapping class determine geometric information about the hyperbolic 3...

It is a classical fact that countable groups of homeomorphisms of the interval and the circle are characterized by purely algebraic properties, namely linear and circular orderability. It remains a difficult and deep problem to understand countable...

The Boone-Higman conjecture (1973) predicts that a finitely generated group has solvable word problem if and only if it embeds in a finitely presented simple group. The "if" direction is true and easy, but the "only if" direction has been open for...

The Oppenheim conjecture, proved by Margulis in 1986, states that for a non-degenerate indefinite irrational quadratic form Q in n≥

3 variables, the image set Q(Zn) of integral vectors is a dense subset of the real line. Determining the distribution...

Motivated by the quantum unique ergodicity conjecture, we examine semiclassical measures for Laplace eigenfunctions on compact hyperbolic n

-manifolds. We prove their support must contain the cosphere bundle of a compact immersed totally geodesic...

The fundamental group of an n-dimensional closed hyperbolic manifold admits a natural isometric action on the hyperbolic space Hn. If n is at most 3 or the manifold is arithmetic of simplest type, then the group also admits many geometric actions on...