Publications & Preprints

[31] Construction of bases for rational and Jordan canonical forms (with Kailiang Lin and Yiqing Sun), preprint.
[30] Rigidity of stable Lyapunov exponents and integrability for Anosov maps (with Shaobo Gan, Ruihao Gu and Yi Shi), preprint.
[29] On the small measure expansion phenomenon in connected noncompact nonabelian groups (with Yifan Jing, Chieu-Minh Tran and Ruixiang Zhang), preprint.
[28] Zimmer's conjecture for non-split semisimple Lie groups (with Aaron Brown and Zhiyuan Zhang), in preparation.
[27] Nondense orbits on homogeneous spaces and applications to geometry and number theory (with Lifan Guan and Dmitry Kleinbock), Ergodic Theory Dynam. Systems, 42 (2022), no. 4, 1327--1372.
[26] Divergent trajectories on products of homogeneous spaces (with Lifan Guan, Antoine Marnat and Ronggang Shi), Adv. Math., 390 (2021), article no. 107910, 33 pp.
[25] Bounded orbits of diagonalizable flows on finite volume quotients of products of SL(2,R) (with Anish Ghosh, Lifan Guan and Tue Ly), Adv. Math. 354 (2019), article no. 106743, 18 pp.
[24] Badly approximable points on planar curves and winning (with Victor Beresnevich and Sanju Velani), Adv. Math. 324 (2018), 148--202.
[23] (survey) Bounded orbits of homogeneous dynamics (with Lifan Guan), Chinese version: Sci. Sin. Math. 47 (2017), no. 12, 1623--1634; English version: Progress Math. 1 (2017), no. 1, 47--62.
[22] 2-dimensional badly approximable vectors and Schmidt's game, Duke Math. J. 165 (2016), no. 2, 267--284.
[21] Bounded orbits of diagonalizable flows on SL(3,R)/SL(3,Z) (with Lifan Guan and Dmitry Kleinbock), Int. Math. Res. Not. IMRN 2015 (2015), no. 24, 13623--13652.
[20] Remarks on minimal sets and conjectures of Cassels, Swinnerton-Dyer, and Margulis (with Barak Weiss), Mosc. J. Comb. Number Theory 3 (2013), no. 3-4, 24--43.
[19] Badziahin-Pollington-Velani's theorem and Schmidt's game, Bull. Lond. Math. Soc. 45 (2013), no. 4, 721--733.
[18] On the dimension datum of a subgroup and its application to isospectral manifolds (with Jiu-Kang Yu and Jun Yu), J. Differential Geom. 94 (2013), no. 1, 59--85.
[17] Rigid geometric structures, isometric actions, and algebraic quotients, Geom. Dedicata 157 (2012), no. 1, 153--185.
[16] Nonabelian harmonic analysis and functional equations on compact groups (with Dilian Yang), J. Lie Theory 21 (2011), no. 2, 427--456.
[15] A Levi-Civita equation on compact groups and nonabelian Fourier analysis (with Dilian Yang), Integral Equations Operator Theory 66 (2010), no. 2, 183--195.
[14] Zero patterns and unitary similarity (with Dragomir Djokovic), J. Algebra 324 (2010), no. 1, 51--80.
[13] Universal subspaces for compact Lie groups (with Dragomir Djokovic), J. Reine Angew. Math. 647 (2010), 151--173.
[12] An implicit function theorem for Banach spaces and some applications (with Karl-Hermann Neeb), Math. Z. 262 (2009), no. 3, 627--643.
[11] Holder stability of diffeomorphisms, Discrete Contin. Dyn. Syst. 24 (2009), no. 2, 315--329.
[10] Nonabelian cohomology of compact Lie groups (with Ming Liu and Zhengdong Wang), J. Lie Theory 19 (2009), no. 2, 231--236.
[09] Topological properties of Ad-semisimple conjugacy classes in Lie groups, J. Lie Theory 18 (2008), no. 3, 541--554.
[08] Holomorphic harmonic analysis on complex reductive groups (with Min Qian and Zhengdong Wang), Acta Math. Sci. Ser. B Engl. Ed. 28 (2008), no. 3, 560--572.
[07] Curve selection lemma for semianalytic sets and conjugacy classes of finite order in Lie groups (with Zhengdong Wang), Sci. China Ser. A 51 (2008), no. 3, 383--388.
[06] Nonabelian cohomology with coefficients in Lie groups (with Zhengdong Wang), Trans. Amer. Math. Soc. 360 (2008), no. 6, 3019--3040.
[05] Twisted Weyl groups of Lie groups and nonabelian cohomology, Geom. Dedicata 128 (2007), no. 1, 167--176.
[04] On the realization of Riemannian symmetric spaces in Lie groups II (with Zhengdong Wang), Topology Appl. 153 (2006), no. 15, 2943--2947.
[03] On the realization of Riemannian symmetric spaces in Lie groups (with Zhengdong Wang), Topology Appl. 153 (2006), no. 7, 1008--1015.
[02] A generalization of random matrix ensemble I: general theory (with Zhengdong Wang and Kuikua Yan), Pacific J. Math. 228 (2006), no. 1, 1--17.
[01] The triviality of the complexified tangent bundles of some manifolds, Adv. Math. (China) 32 (2003), no. 5, 623--628.