Zhenghe's Blog

About me

I am Zhenghe Zhang (张正鹤), currently an assistant professor at Department of Mathematics, UC Riverside. I graduated from Department of Mathematics,  Northwestern University and was a student of Amie Wilkinson and Artur Avila. I am studying 1D discrete ergodic Schrödinger operators. It lies across dynamical systems, spectral theory, and mathematical physics.

Currently, I am focusing on uniform (in energy) positivity and uniform large deviation estimates (LDT) of the Lyapunov exponent for different types of ergodic base dynamics, e.g. quasiperiodic motion (typical elliptic dynamics) and doubling map (typical hyperbolic dynamics). The mechanisms that lead to uniform positivity and uniform LDT detects the dynamical behaviors of the base dynamics in a very subtle way. On the other hand, uniform positivity and LDT implies certain regularity properties of the Lyapunov exponent and are also strong indications of the so called Anderson Localization phenomenon.

I am following my heart to do math.

Click here for my personal webpage.


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