Zhenghe's Blog

About me

I am Zhenghe Zhang (张正鹤), currently a G.C. Evans instructor of Department of Mathematics, Rice University, and working under the supervision of David Damanik. I graduated from Department of Mathematics,  Northwestern University and was a student of Amie Wilkinson and Artur Avila. As you may see from my posts, I am interested in dynamically defined 1D discrete Schrödinger operators. It lies between dynamical systems and spectral theory, both of which are my favorite fields of study.

Currently, I am trying to understand positivity and continuity of the Lyapunov exponent and the IDS, metric structure of spectrum, and Anderson Localization phenomena for smooth quasi-periodic potentials. It’s particularly interesting to see that arithmetic property of the frequencies, largeness of the coupling constant and smoothness of the potentials interact with each other. I am also interested in potentials generated by subshifts or by the doubling map.

I am following my heart to do math.

Click here for my personal webpage.

 

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