Disheng Xu's Homepage
I am an assistant professor at Great Bay University, China. 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 BICMR, 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, dimension theory, holomorphic dynamics.
Spectral theory of Schrödinger operators.
Fractal geometry.
Contact Information:
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.
2020 Autumn: Calculus 1, section 135 ROSE.
2021 Winter: Dynamical Systems for Graduate students.
2021 Autumn: Real analysis.
Conference:
Papers and preprints:
Density of positive Lyapunov exponents for symplectic cocycles.
Journal of European Mathematical Society, Volume 21, Issue 10, 2019, pp. 3143–3190
Uniformly quasiconformal partially hyperbolic systems, with C. Butler.
Annales Scientifiques de l'Ecole Normale Superieure, vol. 51, no. 5, 2018, pp. 1085-1127.
On mixing diffeomorphisms of the disk, with A. Avila, B. Fayad, P. Le Calvez, Z, Zhang.
Inventiones mathematicae, 220 (3), 2020, 673-714.
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, 2018, New Series volume 49, pages 73–87.
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.
Ergodic Theory and Dynamical Systems, Volume 39, Issue 4, April 2019 , pp. 1082-1098.
On classification of higher rank Anosov actions on compact manifold, with D. Damjanovic.
Israel Journal of Mathematics, 2020, 238 (2), 745-806.
Pathology and asymmetry: centralizer rigidity for partially hyperbolic diffeomorphisms, with D. Damjanovic and A. Wilkinson.
Duke Mathematical Journal, 170(17): 3815-3890, 2021.
On conservative partially hyperbolic abelian actions with compact center foliation, with D. Damjanovic.
Centralizers of derived-from-Anosov systems on 𝕋^3: rigidity versus triviality, with S. Gan, Y. Shi and J. Zhang.
Ergodic Theory and Dynamical Systems. Volume 42 , Issue 9 , September 2022 , pp. 2841 - 2865.
Anosov actions: classification and the Zimmer Program, with D. Damjanovic, R. Spatzier and K. Vinhage.
Transitive centralizer and fibered partially systems, with D. Damjanovic and A. Wilkinson.
International Mathematics Research Notices, 2024 (12), 9686-9704.
On the dimension theory of random walks and group actions by circle diffeomorphisms, with W. He and Y. Jiao,
On the dimension of limit sets on PR^3 via stationary measures: the theory and applications, with Jialun Li, Wenyu Pan.
On the dimension of limit sets on PR^3 via stationary measures: variational principles and applications, with Yuxiang Jiao, Jialun Li, Wenyu Pan.
International Mathematics Research Notices, 2024(19), 13015–13045.
Invariant distibutions of partially hyperbolic systems: fractal graphs, excessive regularity, and rigidity,
with Jiesong Zhang. Preprint.
The symmetries of affine K-systems and a program for centralizer rigidity,
with D. Damjanovic, A. Wilkinson and C. Wu. Preprint.
Hyperbolicity for one-frequency analytic quasi-periodic (Hermitian)-symplectic cocycles,
with D. Wang and Q. Zhou. Preprint.