Dynamics and Analysis Seminar

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

Department of Mathematics, CUNY Graduate Center

Spring 2014 Schedule

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


January 29, No Event (First week of the spring semester)

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

February 12, No Event (Lincolnís 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 II

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 23rd, 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. Thurstonís 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.