Wesleyan Dynamics and Analysis (DnA) Seminar

Fall 2017

Tuesdays at 12:00p in Exley 638

Organizers: Ilesanmi Adeboye, Dave Constantine, Adam Fieldsteel, Han Li, Felipe Ramirez

Date Speaker Title and Abstract
Sept 12

Sept 19 Tamara Kucherenko
Measures of maximal entropy for suspension flows over the full shift

We consider suspension flows with continuous roof function over the full shift on a finite alphabet. For any positive entropy subshift of finite type Y, we show there exists a roof function such that the measure(s) of maximal entropy for the suspension flow over the full shift are exactly the lifts of the measure(s) of maximal entropy for Y. In the case when Y is transitive, this gives a unique measure of maximal entropy for the flow which is not fully supported. If Y has more than one transitive component, all with the same entropy, this gives explicit examples of suspension flows over the full shift with multiple measures of maximal entropy. This contrasts with the case of a Hölder continuous roof function where it is well known the measure of maximal entropy is unique and fully supported. This is joint work with Dan Thompson.

Sept 26

Oct 3 No meeting (faculty meeting)

Oct 10

Oct 17 Thang Nguyen
Hyperbolic rank rigidity

Motivated by the question about (Euclidean) rank rigidity, whether a closed nonpositively curved manifold with every geodesic locally contained in a flat is locally symmetric, we consider the question where flat is replaced by hyperbolic plane. The question about Euclidean rank rigidity was answered positive by Ballmann-Brin-Eberline and Burns-Spatzier in 80's. For the later one, it has not been completely solved yet. It was achieved in many cases by Hamenstadt and Constantine. We give a positive answer for the case quarter-pinched manifolds, which we use different technique with the ones of Hamenstadt or Constantine. The main tool is from dynamics of Lyapunov distributions and a lemma by Foulon. I will talk about difficulty and ideas of proofs. This is a joint work with C. Connell and R. Spatzier.

Oct 24 No meeting (Fall Break)

Oct 31 Shahriar Mirzadeh
Dimension estimates for the set of points with non-dense orbit in homogeneous spaces

In this talk we study the set of points in a homogeneous space whose orbit escapes the complement of a fixed compact subset. We find an upper bound for the Hausdorff dimension of this set. This extends the work of Kadyrov, where he found an upper bound for the Hausdorff dimension of the set of points whose orbit misses a fixed ball of sufficiently small radius in a compact homogeneous space. We can also use our main result to produce new applications to Diophantine approximation. This is joint work with Dmitry Kleinbock.

Nov 7

Nov 14 No meeting (faculty meeting)

Nov 21

Nov 28 Scott Zimmerman
An introduction to analysis and geometry in the Heisenberg groups

The Heisenberg group is a Lie Group first described by Herman Weyl and named after Werner Heisenberg (as he was the first to study the Lie algebra associated with the group). Since it's introduction, the Heisenberg group has been an object of interest for many fields in analysis, geometry, and physics. In this talk, I will define the Heisenberg group and provide some of its interesting analytic and geometric properties. As a point of illustration, I will discuss the structure of geodesic curves in the group and present a version of the classical Whitney extension theorem for curves.

Dec 5 No meeting (faculty meeting)