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。

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》

2007.07-2012.12 必赢76net线路数学系 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 必赢76net线路数学系 /必赢国际bwin登录 副教授

2017.12-至今 必赢76net线路 教授

1. The realization of Smale solenoid type attractors in 3-manifolds. (with Ma, jiming) , Topology Appl. 154 (2007), no. 17,3021–3031 Summary MR Article

2. Lorenz like Smale flows on three-manifolds. Topology Appl. 156 (2009), no. 15,2462–2469.Summary MR Article

3. Regular level sets of Lyapunov graphs of nonsingular Smale flows on 3-manifolds. Discrete Contin. Dyn. Syst. 29 (2011), no. 3, 1277–1290. Summary MR Article

4. Genus two Smale-Williams solenoid attractors in 3-manifolds. (with Ma, jiming) , J. Knot Theory Ramifications 20 (2011), no. 6, 909–926. Summary MR Article

5. The templates of non-singular Smale flows on three manifolds. Ergodic Theory Dynam. Systems 32 (2012), no. 3, 1137–1155. Summary MR Article

6. Lyapunov graphs of nonsingular Smale flows on S1×S2. Trans. Amer. Math. Soc. 365 (2013), no. 2, 767–783. Summary MR Article

7. A note on homotopy classes of nonsingular vector fields on S3. C. R. Math. Acad. Sci. Paris 352 (2014), no. 4, 351–355. Summary MR Article

8. Behavior 0 nonsingular Morse Smale flows on S3. Discrete Contin. Dyn. Syst. 36 (2016), no. 1, 509–540. Summary MR Article

9. 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. Summary MR Article

10. Every 3-manifold admits a structurally stable nonsingular flow with three basic sets. Proc. Amer. Math. Soc. 144 (2016), no.11,4949-4957. Summary MR Article

11. Building Anosov flows on 3-manifolds. (with Francois Beguin and Christian Bonatti) Geom. Topol. 21 (2017), no.3, 1837-1930.Summary MR Article

12. Affine Hirsch foliations on 3-manifolds. Algebr. Geom. Topol. 17 (2017), no. 3, 1743-1770.Summary MR Article

1. 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; Mooc教程

2. 拓扑学(数学系本科三年级.秋), 讲义

3. 代数拓扑(数学系研究生,春), 教材:AlgebraicTopology(Allen Hatcher)

法国数学家Etienne.ghys与电脑制图专家Jos.leys等人合作超赞的科普视频：

1. 维数(Dimension)

2. 混沌(Chaos)

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

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