Wesleyan Dynamics and Analysis (DnA) Seminar

Tuesdays at 12:00p in Exley 6??

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

Fall 2018

Date Speaker Title and Abstract
Sept 4 No meeting (faculty meeting)

Sept 11 Dave Constantine
What is a dynamical zeta function?

Sometimes, when one has very smart coauthors, certain theorems appear in one's papers which one has apparently helped prove, but which one does not understand. Sometimes, these statements say things about zeta functions. Being but a humble geometer and dynamicist, sometimes one feels a certain embarrassment having one's name attached to such august mathematical objects. In such a situation, one sometimes feels compelled to try to understand these objects and why they are being used to study dynamics.

On a completely unrelated note, in this talk I'll give a survey of a number of different types of zeta functions which are defined in analogy with number-theoretic zeta functions, and which can all be cast in a common framework as dynamical zeta functions. I'll discuss what these functions are, what properties we want them to have, and what sort of statements these properties imply. I'll discuss zeta functions for graphs, hyperbolic manifolds, and general dynamical systems, and even note an application involving knot theory.

Sept 18

Sept 25

Oct 2

Oct 9

Oct 16 No meeting (faculty meeting)

Oct 23

Oct 30

Nov 6

Nov 13 No meeting (faculty meeting)

Nov 20

Nov 27

Dec 4 No meeting (faculty meeting)

Spring 2019

Date Speaker Title and Abstract
Jan 22 Asaf Katz
University of Chicago
Quantitative disjointness of nilflows and horospherical flows

In his influential disjointness paper, H. Furstenberg proved that weakly-mixing systems are disjoint from irrational rotations (and in general, Kronecker systems), a result that inspired much of the modern research in dynamics. Recently, A. Venkatesh managed to prove a quantitative version of this disjointness theorem for the case of the horocyclic flow on a compact Riemann surface. I will discuss Venkatesh's disjointness result and present a generalization of this result to more general actions of nilpotent groups, utilizing structural results about nilflows proven by Green-Tao-Ziegler. If time permits, I will discuss certain applications of such theorems in sparse equidistribution problems and number theory.

Jan 29

Feb 5 Andrew Zimmer
Louisiana State University
Regularity of limit sets of Anosov representations

Projective Anosov representations are representations of word hyperbolic groups into SL_d(R) with certain dynamical properties. Under some irreducibility conditions, we give necessary and sufficient conditions for when the limit set of such a representation is a C^{1,a} submanifold of projective space. This is joint work with T. Zhang.

Feb 12 No meeting (faculty meeting)

Feb 19

Feb 26

Mar 5 No meeting (faculty meeting)

Mar 12 No meeting (Spring Break)

Mar 19 No meeting (Spring Break)

Mar 26

Apr 2

Apr 9

Apr 16 No meeting (faculty meeting)

Apr 23

Apr 30

May 7