Wesleyan Dynamics and Analysis (DnA) Seminar

Tuesdays at 12:00p in Exley 628

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 29

Monday, Feb 4, 4:30pm
(Note the nonstandard time)
Nikolay Moshchevitin
Moscow State University
Diophantine Approximation

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

Monday, Mar 4, 4:30pm
(note the nonstandard time)
Asaf Katz
University of Chicago
Generalizations of Furstenberg's diophantine result

In his seminal paper from 1967, H. Furstenberg proved his famous x2x3 theorem which states that for every irrational x, the set 2n3mx is dense modulo 1. I will show a couple of generalizations of this result, which imply density of sparser sequences, using earlier works of D. Meiri and M. Boshernitzan. In particular, I will show density modulo 1 of sequences such as 2n33m33k2x, for every irrational x. I will also discuss another result which is concerned with the case where no group action is present. The talk will be accessible, no prior knowledge is assumed.

Mar 12 No meeting (Spring Break)

Mar 19 No meeting (Spring Break)

Mar 26

Apr 2 Caglar Uyanik
Dynamics on geodesic currents and atoroidal subgroups of Out(FN)

Geodesic currents on surfaces are measure theoretic generalizations of closed curves on surfaces and they play an important role in the study of the Teichmuller spaces. I will talk about their analogs in the setting of free groups, and try to illustrate how the dynamics and geometry of the Out(FN) action reflects on the algebraic structure of Out(FN).

Wednesday, Apr 10
Note the nonstandard day!
Dan Alvey
Diophantine properties of affine subspaces of Euclidean space


Apr 16 No meeting (faculty meeting)

Apr 23

Apr 30

May 7