王宏玉-数学学院

王宏玉

发布日期：2018-10-16浏览次数：

王宏玉

数学科学学院扬州大学江苏, 中国 225002 Email: hywang@yzu.edu.cn

1 研究方向

主要研究方向为微分几何, 偏微分方程及低维拓扑. 近年来, 主要从事度量几何, 辛几何和非线性发展方程的研究。

2 教育

(1)北京大学 1984-1988数学系博士生, 主攻非线性分析, 于1988年获博士学位。导师: 张恭庆

(2)南京大学 1982-1984数学系研究生, 主攻微分几何, 于1984年获硕士学位。导师: 黄正中

(3)南京大学 1978-1982数学系本科生, 计算数学专业, 于1982年1月获学士学位.

3 工作经历

(1)1988年末与世界著名数学家 Uhlenbeck 各自独立构造了不稳定 Yang-Mills 场, 并因此应邀去美国哈佛大学数学系做两年博士后, 然后去杜克访问一年.

(2)1991年至2001年在新加坡国立大学从事数学教学和研究, 期间先后访问过日本京都大学, 东京大学, 英国牛津大学, 剑桥大学, 意大利第三世界科学院等世界著名学府.

(3)2001年5月起辞去新加坡国立大学职务, 任扬州大学教授.

(4)2001年9月被南京大学聘为客座教授, 并任南京大学兼职博士生导师.

4 研究成果

已独立或与他人合作取得了多项研究成果. 主要有:

(1)解决Yau问题集中第10个问题, 即Chern-Hopf猜测中的一部分.

(2)利用近复结构的形变, 回答了Donaldson问题: 驯服到相容(tamed to compatible).

(3)广义Calabi-Yau 方程, 四维近复流形上的上同调.

(4)与梅加强等合作给出了 Rn (n>= 3) 极小体积为零的详细证明..

(5)系统地研究了闭流形的微分同胚群与保体积微分同胚群之间的关系, 对著名的 J.Moser 定理给出了另一种证明; 并研究了辛流形上的广义 Calabi-Yau 方程.

(6)给出了 Floer 同调的正合序列定理;

(7)与北京大学丁伟岳, 中科院王友德合作研究了 Schrödinger flow, 深入地研究了取值于 Hermite 对称空间的广义 Heisenberg 模型和相伴于紧 Hermite 李代数的三次非线性 Schrödinger 方程, 给出了两者之间的一一对应, 并由此构造了具体的周期解. 还证明了 Schrödinger 流的整体解的存在性.

(8)系统深入地研究了 Yang-Mills 场及其方程, 探讨了 R4 上经典 Yang-Mills 场的模空间几何, 为 Yang-Mills 方程构造了无穷多个非极小解, 亦即为不稳定 Yang-Mills 方程构造了无穷多个非极小解, 亦即为不稳定 Yang-Mills 场建立了存在性定理, 此结果被收入美国大学物理专业研究生教科书.

5 已发表文章

[1] S. Fang, H. Y. Wang, On non-elliptically symplectic manifolds, arXiv: 1807.00326[math.SG], 2018.

[2] Q.Tan, H.Y. Wang, J.R. Zhou and P. Zhu, On tamed almost complex four manifolds, arXiv: 1712.02948[math.DG], 2017.

[3] Q.Tan, H.Y. Wang, J.R. Zhou, Symplectic parabolicity and $L^2$ symplectic harmonic forms, Quart. J. Math. 70(2019), 147-169.

　[4]Tan, Qiang; Wang, Hongyu; Zhou, Jiuru. A note on the deformations of almost complex structures on compact four-manifolds. (accepted by J. Geom. Anal.)

　[5]Wang, Hongyu. On J-anti-invariant cohomology of compact almost complex four-manifolds and applications (in Chinese). Sci Sin Math, 2016, 46: 697-708, doi: 10.1360/N012015-00348

[6]Tan, Qiang; Wang, Hongyu; Zhou, Jiuru. Primitive cohomology of real degree two on compact symplectic manifolds. Manuscripta Math. 148 (2015), no. 3-4, 535-556.

[7]Tan, Qiang; Wang, Hongyu; Zhang, Ying; Zhu, Peng. On cohomology of almost complex 4-manifolds. J. Geom. Anal. 25 (2015), no. 3, 1431-1443.

[8]Wang, Hong Yu; Zhu, Peng. On a generalized Calabi-Yau equation. Annales l'Institut Fourire, 60 (2010), no. 5, 1595--1615.

[9]Wang, Hong Yu; Zhu, Peng. Local Riemann-Roch theorem for almost Hermitian manifolds. Bull Braz Math Soc, 41 (2010), no. 4, 583--605.

[10]Luo, Jin Quan; Tang, Yuan Sheng; Wang, Hong Yu. Cyclic Codes and Sequences: The Generalized Kasami Case. IEEE Transactions on Infomation Theory, 56 (2010), no. 5, 2130--2142.

[11]Wang, Hong Yu; Zhu, Xiu Juan. On initial data of the monopole equation. Acta Math. Sinica (English series), 25 (2009), no. 12, 2127--2132.

[12]Wang, Hong Yu; Xu, Hai Feng. Minimal volume of the connected sum of Euclidean spaces, Differential Geometry - Dynamical Systems. 11 (2009), 185--194.

[13]Mei, Jia Qiang; Wang, Hong Yu; Xu, Hai Feng. An elementary proof of MinVol(Rn)=0 for n>=3, An. Acad. Brasil. Ciênc. 80 (2008), no. 4, 597--616.

[14]Ding, Wei Yue; Wang, Hong Yu; Wang, You De. Schrödinger flows on compact Hermitian symmetric spaces and related problems. Acta Math. Sin. (Engl. Ser.) 19 (2003), no. 2, 303--312. (Reviewer: Shu-Cheng Chang)

[15]Wang, Hong Yu. Nonlinear Schrödinger systems associated with Hermitian symmetric Lie algebras. Differential geometry and related topics, 237--249, World Sci. Publ., River Edge, NJ, 2002.

[16]Wang, Hong Yu. Geometric nonlinear Schrödinger equations. Integrable systems, topology, and physics (Tokyo, 2000), 313--324, Contemp. Math., 309, Amer. Math. Soc., Providence, RI, 2002. (Reviewer: Leung-Fu Cheung)

[17]Pang, Peter Y. H.; Wang, Hong Yu; Wang, You De. Schrödinger flow on Hermitian locally symmetric spaces. Comm. Anal. Geom. 10 (2002), no. 4, 653--681. (Reviewer: Shu-Cheng Chang)

[18]Wang, Hong Yu; Wang, You De. Global nonautonomous Schrödinger flows on Hermitian locally symmetric spaces. Sci. China Ser. A 45 (2002), no. 5, 549--561. (Reviewer: Shu-Yu Hsu)

[19]Dai, Bo; Wang, Hong Yu. A note on diffeomorphism groups of closed manifolds. Ann. Global Anal. Geom. 21 (2002), no. 2, 135--140. (Reviewer: Nikolai K. Smolentsev)

[20]Pang, P. Y. H.; Wang, H. Y.; Yin, J. X. Free-boundary problem for a singular diffusion equation. J. Math. Anal. Appl. 265 (2002), no. 2, 414--429.

[21]Pang, Peter Y. H.; Wang, Hong Yu; Wang, You De. Schrödinger flow for maps into Kähler manifolds. Asian J. Math. 5 (2001), no. 3, 509--533.

[22]Wang, Hong Yu; Wang, You De. Global inhomogeneous Schrödinger flow. Internat. J. Math. 11 (2000), no. 8, 1079--1114. (Reviewer: Kuppuswamy Porsezian)

[23]Pang, Peter Y. H.; Wang, Hong Yu; Wang, You De. Local existence for inhomogeneous Schrödinger flow into Kähler manifolds. Acta Math. Sin.(Engl. Ser.) 16 (2000), no. 3, 487--504. (Reviewer: Knut Smoczyk)

[24]Li, H. L.; Pang, P. Y. H.; Wang, H. Y.; Yin, J. X. On a partial differential equation arising in electrodiffusion in thin-film conductors. J. Math. Anal. Appl. 232 (1999), no. 1, 20--33.

[25]Wang, Hong Yu. The exactness theorem for Floer homology. Publ. Res. Inst. Math. Sci. 33 (1997), no. 5, 713--750. (Reviewer: David E. Hurtubise)

[26]Wang, Hong Yu. Morse theory and non-minimal solutions to the Yang-Mills equations. Tsukuba J. Math. 21 (1997), no. 3, 567--593.

[27]Wang, Hong Yu. Remarks on the moduli spaces over S4. Far East J. Math. Sci. 3 (1995), no. 2, 229--245. (Reviewer: Antony Maciocia)

[28]Wang, Hong Yu. The construction of isolated reducible SU(2)-connections over S2 X S2. Acta Math. Sinica (N.S.) 8 (1992), no. 1, 60--77. (Reviewer: Xiao Wei Peng)

[29]Wang, Hong Yu. The existence of nonminimal solutions to the Yang-Mills equation with group SU(2) on S2 X S2 and S1 X S3. J. Differential Geom. 34 (1991), no. 3, 701--767. (Reviewer: Jan Segert)

[30]Wang, Hong Yu. A perturbation theorem and stability for a surface with prescribed mean curvature. (In Chinese) Nanjing Daxue Xuebao Shuxue Bannian Kan 1 (1984), no. 2, 189--209. (Reviewer: C.-C. Hsiung)

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