國（境）外文教專家系列講座一百七十七講：加利福尼亞大學河濱分校張正鶴副教授：Positivity and large deviations of the Lyapunov exponents for potentials generated by hyperbolic transformations

發布時間：2023-06-16

一、主講人介紹：張正鶴副教授

張正鶴，加利福尼亞大學河濱分校 Associate Professor ，主要從事動力系統、譜理論和數學物理方向的研究，本科為中國海洋大學2001級數學系學生，碩士師從南京大學尤建功教授，博士就讀于西北大學，師從 Amie Wilkinson 和 Artur Avila ,畢業后曾在萊斯大學從事博士后研究。已在 Invent . Math ., Trans . Amer . Math . Soc ., Comm . Math . Phys ., Int . Math . Res . Not ., J . Funct . Anal ., J . Spectr . Theory 論文。

二、講座信息

In this talk, I will introduce some recent joint work with A. Avila and D. Damanik in showing positivity and large deviations of the Lyapunov exponent for Schrodinger operators with potentials generated by hyperbolic transformations. Specifically, we consider the base dynamics which is a subshift of finite type with an ergodic measure admitting a bounded distortion property and which has a fixed point. We show that if the potentials are locally constant or globally fiber bunched, then the set of zero Lyapunov exponent is finite. Moreover, we have a uniform large deviation estimate away from this finite set. As a consequence, we obtain full spectral Anderson localization for such potentials.

時間：2023年6月27日15:30-16:30

地點：數學院424會議室

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