研究方向
基础数学:低维拓扑上的叶状结构、动力力系统。特别是taut叶状结构、Anosov流、Smale流与纽结论、扩张吸引子的整体实现、拓扑等价分类。
教育背景
1998-2002,武汉大学数学与统计学院,数学基地班 本科
2002-2007,北京大学数学与科学学院,方向:低维拓扑 博士
博士论文:《螺线圈作为三维流形中的吸引子》
工作经历
2007.07-2012.12 同济大学数学系 讲师
2011-2012 法国勃艮第数学研究所(IMB) 国家公派博士后
2012.12-2017.12 同济大学数学系 /探花视频
副教授
2017.12-至今 探花视频
教授
论文与出版物
The realization of Smale solenoid type attractors in 3-manifolds. (with Ma, jiming) , Topology Appl. 154 (2007), no. 17,3021–3031
Lorenz like Smale flows on three-manifolds. Topology Appl. 156 (2009), no. 15,2462–2469.
Regular level sets of Lyapunov graphs of nonsingular Smale flows on 3-manifolds. Discrete Contin. Dyn. Syst. 29 (2011), no. 3, 1277–1290.
Genus two Smale-Williams solenoid attractors in 3-manifolds. (with Ma, jiming) , J. Knot Theory Ramifications 20 (2011), no. 6, 909–926.
The templates of non-singular Smale flows on three manifolds. Ergodic Theory Dynam. Systems 32 (2012), no. 3, 1137–1155.
Lyapunov graphs of nonsingular Smale flows on S1×S2. Trans. Amer. Math. Soc. 365 (2013), no. 2, 767–783.
A note on homotopy classes of nonsingular vector fields on S3. C. R. Math. Acad. Sci. Paris 352 (2014), no. 4, 351–355.
Behavior 0 nonsingular Morse Smale flows on S3. Discrete Contin. Dyn. Syst. 36 (2016), no. 1, 509–540.
A spectral-like decomposition for transitive Anosov flows in dimension three. (with Francois Beguin and Christian Bonatti) Math. Z. 282 (2016), no.1, 509-540.
Every 3-manifold admits a structurally stable nonsingular flow with three basic sets. Proc. Amer. Math. Soc. 144 (2016), no.11,4949-4957.
Building Anosov flows on 3-manifolds. (with Francois Beguin and Christian Bonatti) Geom. Topol. 21 (2017), no.3, 1837-1930.
Affine Hirsch foliations on 3-manifolds. Algebr. Geom. Topol. 17 (2017), no. 3, 1743-1770.
主讲以下课程
高等数学A(本科一年级,春秋), 相关网站: 同济高数同步课程网;
拓扑学(数学系本科三年级.秋), 讲义
代数拓扑(数学系研究生,春), 教材:(Allen Hatcher)
法国数学家与电脑制图专家等人合作超赞的科普视频:
研究情况
Recently, I'm working on the topics related to:
banched surface, expanding attractor (of flow), folaition and lamination topology of 3-manifold, see for instance, Chr, FO, Oe, Li
Recently, I'm intersted in:
General theory about Foliation and Lamilation theory on 3-manifolds, see for instance, Nov, Ga1, Ga2, Ga3, GaOe, Brit, BooGa
Circle diffeomorphisms, see for instance, Na, Gh
Links
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可以下载、上传数学学术论文
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