**Dynamics and
Analysis Seminar**

Organized by Yunping
Jiang (yunping.jiang@qc.cuny.edu)
with Fred Gardiner and Linda Keen

Department
of Mathematics

Wednesday,
1:30pm-3:00pm (__Math Thesis Room, Rm. 4214-03)__:

February 5, Yunping Jiang, Thurston program for meromorphic and entire functions (following Jeremy
Kahn’s lecture)

February 12, No Event (Lincoln’s Birthday)

February 19, Tao Chen, Levy Cycle for exponential
family

February 26, Linda Keen, On complex tangent family

March 5, Tao Chen, Levy cycle for exponential
family

March 12, (no event, YPJ
will be UMA)

March 19, Linda
Keen, On complex tangent family

March 26, Zhiren Wang
(Yale Univ.) Title: Global rigidity of abelian
Anosov actions

Abstract: As part of a more general conjecture by Katok and Spatzier,

it was asked if all smooth Anosov
$Z^r$-actions on tori, nilmanifolds

and infranilmanifolds
without rank-1 factor actions are, up to smooth conjugacy,

actions by automorphisms.
In this talk, we will discuss a recent joint work with

Federico Rodriguez Hertz that affirmatively answers this question.

April 2, Gangotryi Sorcar (SUNY at Binghamton), Title: Teichmuller space of negatively curved
manifolds

Abstract: In
this talk I will give an overview of existing results on

the non-contractibility of the Teichmuller space of hyperbolic manifolds

and also talk about some similar new findings on Gromov-Thurston

manifolds $M$
that are not hyperbolic but negatively curved.

I will outline the construction of a non-trivial element in

$\pi_{**1}**
({\mathcal T}^{\infty}
(M))$, where ${\mathcal T}^{\infty}(M)$

denotes the Teichmuller
space of all negatively curved Riemannian

metrics on $M$, which is the quotient space of the space of
all negatively

curved Riemannian metrics on $M$ modulo the
space of all isotopies of $M$

that are homotopic to
the identity. Time permitting, I will also talk about the

higher homotopy groups of ${\mathcal T}^{\infty}(M)$.

April 9, QuanLie Fan, Title: On some
problems in multivariable operator theory.

Abstract: Multivariable
operator theory, the study of several operators

or an algebra of operators at a time, started
more recently compared to

classical single variable operator theory on
Hilbert spaces.

In this talk we will give an introduction of multivariable operator
theory.

We will discuss problems on some reproducing Kernel Hilbert spaces

and the interplay between harmonic analysis and
operator theory.

April 23, Alexander
Kheyfits, Distribution of zeros of entire and
analytic functions.

April 30, Zhe Wang
(BC), Teichmuller theory and quadratic
differentials I

May 7, Yunchun
Hu (for thesis defense)

May 14, No Event (YPJ will be Taiwan)

May 23 (Notice on different day and time):
Zhiqiang Li (UCLA)

Date: Friday, May 23^{rd},
2014, Time: 11am-12:30pm, Place: Math Thesis Room

Title : Thermodynamical formalism for expanding
Thurston maps

Abstract: Thurston maps are a class of
branched covering maps on the 2-sphere that arose

in W.
Thurston’s characterization of postcritically finite
rational maps.

By imposing a natural expansion
condition, M. Bonk and D. Meyer investigated

a subclass
of Thurston maps known as expanding Thurston maps, which turned

out to
enjoy nice topological, metric, and dynamical properties. Thermodynamical
formalism

has
been a powerful tool, for many classical dynamical systems, to investigate
invariant measures

whose Jacobian functions have strong regularity properties. In
this talk, we will first introduce

expanding
Thurston maps with some motivation from their connection to other topics of
mathematics.

We will then use thermodynamical formalism to sketch a proof for the
existence, uniqueness,

and
exactness of equilibrium states for expanding Thurston maps and H¨older continuous potentials.

If time permits, we will also
show that an expanding Thurston map is asymptotically **h**-expansive

if and
only if it has no periodic critical points, which suggests the subtlety of our
notion of expansion.