人物經歷
現任南開大學陳省身數學研究所教授、博士生導師 。1983年畢業於徐州師範學院﹔1989年獲北京大學理學博士學位,1989-1991年在南京大學做博士後,1986年獲南京大學理學碩士學位﹔1989年獲北京大學理學博士學位後到南京大學任教,任數學系系主任。1994年2月8日訪問瑞士蘇黎世高工(ETH)數學研究所﹔1995年至1997年受德國洪堡基金會資助在科隆大學和慕尼黑工業大學做合作研究﹔1998年2月至8月在羅馬第三大學做訪問教授。1998年成為國家非線性科學攀登項目組正式成員﹔1999年獲得國家傑出青年基金﹔2000年成為國家重點基礎研究發展規劃項目組(非線性科學)成員。
1991年起歷任南京大學講師、副教授、教授、博士生導師、長江學者、數學系主任,2016年起任南開大學陳省身數學研究所教授、博士生導師。曾在德國科隆大學和慕尼黑工大做洪堡學者;曾訪問瑞士蘇黎世高工(ETH)數學研究所等多所國外著名大學。在Duffing方程的穩定性,KAM理論,哈密頓偏微分方程的擬周期運動、薛丁格運算元的譜理論等方面做出了一系列深刻的工作。
2018年8月1日至8月9日,第28屆國際數學家大會於在巴西里約熱內盧召開,尤建功教授應邀參加第28屆國際數學家大會並於2日作45分鐘特邀報告,報告題目為“定量幾乎可約性理論及其套用”,主要介紹尤建功教授與合作者在擬周期線性系統可約性及其在運算元譜理論中的套用方面的一些成果。這是自2002年以來,繼龍以明院士、張偉平院士之後,南開學者又一次應邀在國際數學家大會上作主題報告。
國際數學家大會(International Congress of Mathematicians,簡稱ICM)是由國際數學聯盟主辦的全球性數學學術會議,是國際數學屆的盛會,每四年舉辦一次。會議的主要內容是進行學術交流,並在開幕式上頒發菲爾茲獎(1936年起)、奈望林納獎(1982年起)、高斯獎(2006年起)和陳省身獎(2010年起)。首屆國際數學家大會於1897年在瑞士蘇黎世舉行,至今共舉辦了27屆。1900年巴黎大會之後,除兩次世界大戰期間外,國際數學家大會從未中斷,2002年在中國北京舉辦了第24屆大會。
在每屆數學家大會上,組委會都會邀請一批在相關領域做出傑出工作的著名數學家作主題報告,這標誌著數學家的工作得到了國際數學界的普遍認可和讚譽,同時,對於數學家而言,也是非常高的榮譽。
任免信息
2017年12月,當選中國民主同盟第十二屆中央委員會委員。
研究方向
主要是動力系統﹐特別是Hamilton動力系統。
主要貢獻
現承擔國家基金委重點項目和國家重大基礎研究規劃項目。
研究成果主要集中在KAM理論及其在常微分方程和偏微分方程中的套用方面﹔對低維環面的KAM理論做出了重要發展﹐在第一Melnikov非共振條件下得到了不變環面的存在性﹐並用於研究了國際上非常活躍的Hamilton偏微分方程的擬周期解問題﹔研究成果否定了1994年菲爾茨獎獲得者Bourgain認為KAM理論不能用於重法頻率的看法﹔解決了KAM理論創始人之一Moser關於擺方程Lagrange穩定性的一個公開問題﹔受到了國際同行的重視和好評。
學術論文
Persistence of lower dimensional tori under the first Melnikov's non-resonance condition, to appear in Journal de Mathematiques Pures et Appliquees, 2001(with J.Xu).
1.Persistence of lower dimensional tori under the first Melnikov's non-resonance condition, to appear in Journal de Mathematiques Pures et Appliquees, 2001(with J.Xu).
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, 209–260. 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, 5361–5402. 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, 2385–2395.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, 441–454.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, 831–866. Article; E-Journal.
H. He and J. You
The rigidity of reducibility of cocycles on SO(N ,R). Nonlinearity 21 (2008),no. 10, 2317–2330. Article; E-Journal.
X. Hou and J. You
Diophantine vectors in analytic submanifolds of Euclidean spaces. Sci. China Ser. A. 50 (2007), no. 9, 1334–1338. 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, 375–387] 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, 609–622. Article; E-Journal.
J. Xu and J. You
KAM Tori for Higher Dimensional Beam Equation with Constant Potentials, Nonlinearity 19 (2006), no. 10, 2405–2423. 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, 227–234. 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, 199–204. 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.
教學
•Mathematical Analysis (Fall 2005-2008, undergraduate freshman courses).
•Geometrical Methods in the Theory of Ordinary Differential Equations (Fall 2009-2011, undergraduate junior courses).
•Seminar of Dynamical Systems (Spring 2011-2014, undergraduate junior courses).
•Dynamical Systems (Spring 2008-2010, graduate courses).
•Differential Dynamical Systems (Spring 2011, graduate course).
•Hamiltonian Systems and N-Body Problems(Spring 2012, graduate course).
•Chaos in Dynamical Systems (Spring 2013, graduate course).
獲獎記錄
曾獲得國家傑出青年基金、香港求是科技基金會傑出青年學者獎、中國高校科技進步獎一等(排名第二)、第六屆江蘇省青年科技獎、國家自然科學二等獎(排名第三)。