I am an assistant professor at Beijing International Center for Mathematical Research, Peking University, starting from August 2020. I obtained my Ph.D degree in October 2016 from Université Paris Diderot and Institut de mathématiques de Jussieu, under the supervision of Professor Artur Avila and Julie Déserti.

I had previously worked at Imperial College London (supervised by Davoud Cheraghi) , the University of Chicago (supervised by Prof. Amie Wilkinson) and KTH in Stockholm (supervised by Prof. Danijela Damjanovic).

Research Interests

• Dynamical systems: Cocycles and associated Lyapunov exponents, rigidity phenomenon, partially hyperbolic systems, higher rank group actions, random dynamics, etc.

• Spectral theory of Schrödinger operators.

Contact Information

Office: 78405 at BICMR.

Email: dishengxu1989 at gmail dot com.

Teaching

• 2018 Winter: Math 27300 Basic Theory of Ordinary Differential Equations.

• 2018 Winter: Math 20100 Mathematical Methods for Physical Sciences II.

• 2018 Spring: Math 20510 (31&41) Analysis in R^n, accelerated.

• 2018 Spring: Training for IMC (International mathematical competition for university students), E 308, 6-7pm every Wednesday.

• 2018 Autumn: Math 20000 (11&80).

• 2019 Spring: Math 20100 (45&53)

• 2020 Winter: Rigidity of abelian Anosov action. Huxley 642, 11AM-1PM every Friday. Office hour: 10AM-11AM every Monday.

• 2020 Autumn: Calculus 1, section 135 ROSE.

• 2021 Winter: Dynamical Systems for Graduate students in Peking University.

Papers

• Density of positive Lyapunov exponents for symplectic cocycles, JEMS, Volume 21, Issue 10, 2019, pp. 3143–3190

• Uniformly quasiconformal partially hyperbolic systems, with C. Butler. Annales de l'ENS, fascicule 5 septembre-octobre 2018.

• On mixing diffeomorphisms of the disk, with A. Avila, B. Fayad, P. Le Calvez, Z, Zhang, to appear in Inventiones Mathematicae.

• Positivity of the Top Lyapunov Exponent for Cocycles on Semisimple Lie Groups over Hyperbolic Bases. with M. Bessa, J. Bochi, M. Cambrainha, C. Matheus, P. Varandas, Bulletin of the Brazilian Mathematical Society, New Series volume 49, pages 73–87(2018)

• Diffeomorphism group valued cocycles over higher-rank abelian Anosov actions, with D. Damjanovic, Ergodic Theory and Dynamical Systems, Volume 40, Issue 1 January 2020 , pp. 117-141.

• Singular analytic linear cocycles with negative infinite Lyapunov exponents, with C. Sadel, ETDS, Volume 39, Issue 4, April 2019 , pp. 1082-1098.

• On classification of higher rank Anosov actions on compact manifold, with D. Damjanovic, to appear in Israel Journal of Mathematics.

• Pathology and asymmetry: centralizer rigidity for partially hyperbolic diffeomorphisms, with D. Damjanovic and A. Wilkinson, preprint.

• On conservative partially hyperbolic abelian actions with compact center foliation, with D. Damjanovic, preprint.

• Centralizers of derived-from-Anosov systems on 𝕋3: rigidity versus triviality, with S. Gan, Y. Shi and J. Zhang.