Zhenghe Zhang

Assistant professor
Office: Surge 256
Phone: 951-827-3210
Email: zhenghe.zhang@ucr.edu



Seminar

Starting Spring 2018, I am running a seminar entitled "Ergodic Theory and Spectral Theory".
Click the title in the line above
 for schedule of talks.

Research Interests

My research interests center around the dynamical object, the Lyapunov exponent, and lie across dynamical systems, spectral theory, 
and mathematical physics. Concretely, I study spectral analysis of ergodic type of Schrodinger operators.

Currently, I am focusing on uniform positivity and uniform large deviation estimates for the associated Lyapunov exponent for various
types of ergodic base dynamics, where uniformities are in the energy parameter. The two properties immediately imply certain regularities 
of the Lyapunov exponent and are strong indications of the Anderson Localization phenomenon.

Examples of ergodic base dynamics I am interested in are irrational rotations on the unit circle (also called quasiperiodic motion, typical 
elliptic dynamics) or the doubling map (typical hyperbolic dynamics). By comparing the mechanisms that lead to uniform positivity and 
LDT of the Lyapunov exponent over these two types of base dynamics, one may detect the huge gap between almost periodic dynamics 
and strongly mixing dynamics as well as the big difference between elliptic dynamics and hyperbolic dynamics.

Papers 

The following papers are or will be available on my arXiv.org page.

  Publications:
  Preprints:
  Papers in Preparation:
  • Work related to positivity, continuity, and LDT of the Lyapunov exponent and Anderson Localization for
    potentials generated by hyperbolic base dynamics (with A. Avila and D. Damanik).     

Teaching:
  • Math 046-Introduction to Ordinary Differential Equations, Summer 2018(upcoming)
  • Math 260 Seminar-Ergodic Theory and Spectral Theory, Spring 2018
  • Math 046-Introduction to Ordinary Differential Equations, Spring 2018
  • Math 046-Introduction to Ordinary Differential Equations, Winter 2018
  • Math 151A-Advanced Calculus I, Fall 2017

  Past Teaching at Rice University (2014-2017):
  • Math 211-Ordinary differential equations and linear algebra, Spring 2017
  • Math 382-Complex analysis, Spring 2017
  • Math 521-Advanced topics in real analysis, Fall 2016
  • Math 435-Dynamical systems, Spring 2016
  • Math 523-Functional analysis, Fall 2015
  • Math 211-Ordinary differential equations and linear algebra, Fall 2015
  • Math 112-Calculus and its applications, Spring 2015
  • Math 322-Introduction to analysis II, Spring 2015
  • Math 211-Ordinary differential equations and linear algebra, Fall 2014
Meetings 
Links





since 10/27/2014