曾任南京大学数学系主任、教授、博士生导师。

1983年毕业于徐州师范学院﹔

1986年获南京大学理学硕士学位﹔

1989年获北京大学理学博士学位后到南京大学任教。

1994年2月8日访问瑞士苏黎世高工（ETH）数学研究所﹔

1995年至1997年受德国洪堡基金会资助在科隆大学和慕尼黑工业大学做合作研究﹔

1998年2月至8月在罗马第三大学做访问教授；

1998年成为国家非线性科学攀登项目组正式成员﹔

1999年获得国家杰出青年基金﹔

2000年成为国家重点基础研究发展规划项目组（非线性科学）成员；

2016年9月，担任南开大学陈省身数学研究所教授、博士生导师。

2017年12月，当选中国民主同盟第十二届中央委员会委员。

主要是动力系统﹐特别是Hamilton动力系统。研究成果主要集中在KAM理论及其在常微分方程和偏微分方程中的应用方面﹔对低维环面的KAM理论做出了重要发展﹐在第一Melnikov非共振条件下得到了不变环面的存在性﹐并用于研究了国际上非常活跃的Hamilton偏微分方程的拟周期解问题﹔研究成果否定了1994年菲尔茨奖获得者Bourgain认为KAM理论不能用于重法频率的看法﹔解决了KAM理论创始人之一Moser关於摆方程Lagrange稳定性的一个公开问题﹔受到了国际同行的重视和好评。

2.KAM theory for lower dimensional tori of nearly integrable Hamiltonian systems, Progress in Nonlinear Analysis, edited by K-C. Chang and Y. Long, World Scientific, 2000, 409-423.

3.KAM tori for 1D nonlinear wave equations with periodic boundary condition, Communications in Mathematical Physics., Vol. 211(2), 497-525, 2000(with l, Chierchia).

4.Perturbations of lower dimensional tori for Hamiltonian systems, Journal Of Differential Equations, Vol. 152, 1-29, 1999.

5.A KAM theorem for hyperbolic type degenerate lower dimensional tori in Hamiltonian systems, Communications in Mathematical Physics, Vol. 192. 145-168, 1998.

Almost reducibility and non-perturbative reducibility of quasi-periodic linear systems. Invent. Math. 190 (2012), no. 1, 209u2013260. Article; E-Journal.　　X. Hou and J. You

An infinite dimensional KAM theorem and its application to the two dimensional cubic Schrödinger equation. Adv. Math. 226 (2011), no. 6, 5361u20135402. Article; E-Journal.　　J. Geng, X. Xu and J. You

Persistence of the non-twist torus in nearly integrable Hamiltonian systems. Proc. Amer. Math. Soc. 138 (2010), no. 7, 2385u20132395.Article; E-Journal.　　J. Xu and J. You

Local rigidity of reducibility of analytic quasi-periodic cocycles on U(n). Discrete Contin. Dyn. Syst. 24 (2009), no. 2, 441u2013454.Article; E-Journal.　　X. Hou and J. You

Corrigendum for the paper: "Two-dimensional invariant tori in the neighborhood of an elliptic equilibrium of Hamiltonian systems" in Acta Mathematica Sinica, English Series August 2009, Volume 25, Issue 8, pp 1363-1378. Article　　H. Lu and J. You

Two-dimensional invariant tori in the neighborhood of an elliptic equilibrium of Hamiltonian systems. Acta Mathematica Sinica, English Series August 2009, Volume 25, Issue 8, pp 1363-1378. Article; E-Journal.　　H. Lu and J. You

Full measure reducibility for generic one-parameter family of quasi-periodic linear systems. J. Dynam. Differential Equations 20 (2008), no. 4, 831u2013866. Article; E-Journal.　　H. He and J. You

The rigidity of reducibility of cocycles on SO(N ,R). Nonlinearity 21 (2008),no. 10, 2317u20132330. Article; E-Journal. 　　X. Hou and J. You

Diophantine vectors in analytic submanifolds of Euclidean spaces. Sci. China Ser. A. 50 (2007), no. 9, 1334u20131338. Article; E-Journal.　　R. Cao and J. You

Corrigendum for the paper: "Invariant tori for nearly integrable Hamiltonian systems with degeneracy" [Math. Z. 226 (1997), no. 3, 375u2013387] by Xu, You, and Q. Qiu. Math. Z. 257 (2007), no. 4, 939. Article; E-Journal.　　J. Xu and J. You

Gevrey-smoothness of invariant tori for analytic nearly integrable Hamiltonian systems under Rüssmann’s non-degeneracy condition. J. Differential Equations 235 (2007), no. 2, 609u2013622. Article; E-Journal.　　J. Xu and J. You

KAM Tori for Higher Dimensional Beam Equation with Constant Potentials, Nonlinearity 19 (2006), no. 10, 2405u20132423. Article; E-Journal.　　J. Geng and J. You

The Existence of Integrable Invariant Manifolds of Hamiltonian Partial Differential Equations, Discrete and Continuous Dynamical Systems 16 (2006), no. 1, 227u2013234. Article; E-Journal.　　R.Cao and J. You

An Improved Result for Positive Measure Reducibility of Quasi- periodic Linear Systems, Acta Mathematica Sinica (English series) 22 (1), 2006, 77-86. Article; E-Journal.　　H. He and J. You

A KAM Theorem for Partial Differential Equations in Higher Dimensional Space, Communications in Mathematical Physics, Vol.262(2), 2006, 343-372. Article; E-Journal.　　J.Geng and J.You

Umbilical Torus Bifurcations in Hamiltonian Systems, J. Differential Equations, Vol. 222(1), 2006, 233-262. Article; E-Journal.　　H. Broer, H. Hanssmann and J. You

A simple proof of diffusion approximations for LBFS re-entrant lines, Oper. Res. Lett., 34(2006), no. 2, 199u2013204. Article; E-Journal.　　J. Yang, J.G. Dai, J. You and H. Zhang

Quasi-Periodic Solutions for 1D Schrödinger Equations with Higher Order Nonlinearity, SIAM J. Mathematical Analysis, 36(2005), 1965-1990. Article; E-Journal.　　Z. Liang and J. You

Bifurcations of Normally Parabolic Tori in Hamiltonian Systems, Nonlinearity, 18 (2005) 1735-1769. Article; E-Journal.　　H. Broer, H. Hanssmann and J. You

A KAM Theorem for One Dimensional Schrödinger Equation with Periodic Boundary Conditions, J. Differential Equations, 209, 2005, 1-56. Article; E-Journal.　　J. Geng and J. You

KAM tori of Hamiltonian perturbations of 1D linear beam equations, J.Math.Anal.Appl., 277, 2003, 104-121. Article; E-Journal.　　J. Geng and J. You

A Symplectic Map and its Application to the Persistence of Lower Dimensional InvariantTori, Science in China, 45(5), 2002,598-603. Article; E-Journal.

曾获得国家杰出青年基金、香港求是科技基金会杰出青年学者奖、中国高校科技进步奖一等（排名第二）、第六届江苏省青年科技奖、国家自然科学二等奖（排名第三）。