BGD @ BNU 2023.03.18
Beijing Geometry Day
The aim of the workshops is to promote the communication and improve the understanding of recent progress in geometry.
Date: March 17 to March 19, 2023
Host: Beijing Normal University
Scientific Committee (学术委员会):
Fuquan Fang (Capital Normal University)
Gang Tian (Peking University)
Organizing Committee (组委会):
Jianquan Ge (Beijing Normal University)
Haizhong Li (Tsinghua University)
Zhenlei Zhang (Capital Normal University)
Xiaohua Zhu (Peking University)
Speakers (报告人)：
Wen Shen (Capital Normal University)
Yao Wan (Tsinghua University)
Kewei Zhang (Beijing Normal University)
Shengxuan Zhou (Peking University)
Accommodation (住宿):
Wukuangjunlan Hotel （五矿君澜酒店，北京市海淀区北安河路55号院1号楼）
Registration(注册)：
March 17th -18th : Wukuangjunlan Hotel Conference Room （五矿君澜酒店会议室）
Departure(离开)：
March 18th-19th
Contact:
Jianquan Ge (葛建全) Tel：13811855525 Email: jqge@bnu.edu.cn
Schedule (会议日程)
Beijing Geometry Day
March 18, 2020
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9:00-9:50 Registration
9:50-10:00 Opening speech
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10:00-11:00 Kewei Zhang (张科伟 Beijing Normal University)
A pluripotential approach to the Kahler-Einstein problem
11:00-11:20 Tea break and Photo
11:20-12:20 Shengxuan Zhou (周胜铉 Peking University)
Peak sections and Bergman kernels on complex hyperbolic cusps
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12:20-14:00 Lunch ( buffet )
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14:00-15:00 Yao Wan (万耀 Tsinghua University)
Classification of solutions for the planar isotropic Lp dual Minkowski problem
15:00-15:30 Tea break
15:30-16:30 Wen Shen (沈文 Capital Normal University)
Topological classification of Bazaikin spaces
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16:30-17:00 Free discussion
17:00-17:30 Closing Remark and departure
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Titles and Abstracts
1. Speaker: Kewei Zhang 张科伟（北京师范大学）
Title: A pluripotential approach to the Kahler-Einstein problem
Abstract: Searching for Kahler-Einstein metrics on Fano manifolds is an important problem in geometric analysis. By Tian’s solution of the YTD conjecture, it is known that a K-stable Fano manifold always admits a KE metric. In this talk I will present a pluripotential approach to this problem. More precisely, we show that a Fano manifold admits a unique KE metric if and only if its delta invariant is bigger than 1. This is a joint work with T. Darvas.
2. Speaker: Shengxuan Zhou 周胜铉（北京大学）
Title: Peak sections and Bergman kernels on complex hyperbolic cusps
Abstract: The asymptotic behavior of Bergman kernel on Kahler manifold has been studied by Tian, Ruan, Zelditch, Catlin, Ma, Marinescu and many others since 1990. The works related to Bergman kernel plays an important role in complex geometry. In this talk, we will introduce a way to localize the Bergman kernel by using peak sections. As an application, we consider the asymptotic behavior of Bergman kernels on complex hyperbolic cusps.
3. Speaker: Yao Wan 万耀（清华大学）
Title: Classification of solutions for the planar isotropic Lp dual Minkowski problem
Abstract: The Lp dual Minkowski problem is one of the major problems in convex geometry, which unifies the Lp Minkowski problem and the dual Minkowski problem. In this talk, we introduce our recent work on the complete classification of the solutions of the planar isotropic Lp dual Minkowski problem for any real numbers p, q. This is a joint work with Prof. Haizhong Li.
4. Speaker: Wen Shen 沈文（首都师范大学）
Title: Topological classification of Bazaikin spaces
Abstract: Manifolds with positive sectional curvature have been a central object dates back to the beginning of Riemannian geometry. Up to homeomorphism, there are only finitely many examples of simply connected positively curved manifolds in all dimensions except in dimension 7 and 13, namely, Aloff-Wallach spaces and Eschenburg spaces in dimension 7, and the Bazaikin spaces in dimension 13. The topological classification modelled on the 7-dimensional examples has been carried out by Kreck-Stolz which leads to a complete solution for the Aloff-Wallach spaces. The main goal of this report is to discuss the topological classification problem of the Bazaikin spaces.
