中国人民大学数学学院

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14-09-2020

（几何与拓扑研讨班持续更新）双曲几何与低维拓扑联合讨论班

报告1:

题目：The Mcshane Identity

主讲人：冯可副教授 (电子科技大学)

时间: 2020年9月16日，周三，19:00-21:00

会议号：70493356795

密码: 123456

简介：I will introduce the proofs of the Mcshane identity for one cusped sphere，including Mcshane's idea and Bowditch's.

讨论班简介：本讨论班由人大，北大，复旦，电子科大，华中科大等多校联合组成。研讨内容既有双曲几何、低维拓扑领域的前沿热点问题，同时也涵盖三维几何拓扑的基础理论，旨在培养几何拓扑方向的青年教师、博士后及研究生。

报告2:

题目：The space of hyperbolic manifolds and the volume function（1）

主讲人：靳晓尚（华中科技大学）

时间: 2020年9月24日，周四，19：00--21:00

Abstract: In this seminar, we will study the following two things: --the topological structure on the space 'Hn' where 'Hn' is the set of all n-dimensional complete hyperbolic manifolds up yo isometry,--the properties of the volume function 'vol' on the space 'Hn'. Reference: Riccardo Benedetti, Carlo Petronio, Lectures on Hyperbolic Geometry, chapter E.

报告3:

Speaker: 靳晓尚（华中科技大学）

Time: 10月8日，周四，19：00--21:00

Title: The space of hyperbolic manifolds and the volume function（2）

报告4：

Speaker: 沈良明副教授（北京航空航天大学）

Time: 10月15日，周四，19：00--21:00

Title: Complete Calabi-Yau metrics on Quasi-projective manifolds

Abstract: We first review the results of Tian-Yau on the construction of complete Ricci flat metrics on quasi-projective manifolds. Then we will summerize some works on this aspect since Tian-Yau. Finally we will talk a bit about some recent progress.

报告5:

Speaker: 李畅（中科院数学与系统科学研究院）

Title: A characterization of compact convex polyhedra in hyperbolic 3-space

Abstract: In this seminar, we study the extrinsic geometry of convex polyhedral surfaces in three-dimensional hyperbolic space. We obtain a number of uniqueness results, and also obtain a characterization of the shapes of convex polyhedra in H^3 in terms of a generalized Gauss map. This characterization greatly generalizes Andreev's Theorem.

Reference: I. Rivin and C. D. Hodgson, A characterization of compact convex polyhedra in hyperbolic 3-space, Invent. Math. 111 (1993), no. 1, 77–111.

报告6:

Speaker: 李畅（中科院数学与系统科学研究院）

Title: A characterization of ideal polyhedra in hyperbolic 3-space

Time: 10月29日，周四，19：00--21:00

Abstract: In this seminar, we provide a characterization of dihedral angles of convex ideal (those with all vertices on the sphere at infinity) polyhedra in H^3, and also of those convex polyhedra with some vertices on the sphere at infinity and some in the finite part of H^3. The results of this paper grow out of the general framework of the author's doctoral dissertation.

Reference: Rivin, Igor, A characterization of ideal polyhedra in hyperbolic 3-space, Ann. of Math. (2) 143 (1996), no. 1, 51–70.

报告7:

Speaker: 冯可副教授 (电子科技大学)

Title: Combinatorial Ricci flows and the hyperbolization of a class of compact 3-manifolds

Time: 11月12日，周四，19：00--21:00

Abstract: Thurston conjectured that all compact hyperbolic 3-manifolds can be geometrically triangulated. Under suitable combinatorial assumptions, we confirm this conjecture for such manifolds with higher genus boundary components. This is joint work with Huabin Ge and Bobo Hua.

报告8:

Speaker: 郑涛副研究员 (北京理工大学)

Title: Notions Related to Negativity on Kahler Manifolds and Geometric Applicationsds

Time: 11月19日，周四，19：00--21:00

Abstract: A recent celebrated theorem of Diverio-Trapani and Wu-Yau states that a compact Kahler manifold admitting a Kahler metric of quasi-negative holomorphic sectional curvature has an ample canonical line bundle, confirming a conjecture of Yau. In this talk, we shall introduce a natural notion of almost quasi-negative holomorphic sectional curvature and extend this theorem to compact Kahler manifolds of almost quasi-negative holomorphic sectional curvature. This is a joint work with Yashan Zhang.