Geometric Analysis Seminar at BICMR

Academic Year 2025-26

Fall Semester

Organizers: Gang Tian, Xiaohua Zhu, Bin Zhou, Jianchun Chu

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The seminar usually holds on Wednesday from 9:00-10:00 online. For more details, please visit here.

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Schedule

• Wednesday, September 10, 9:00-10:00, Zoom link (ID: 828 4077 1514, Code: 083690)
  Chao Li (Courant Institute of Mathematical Sciences, New York University) - On the topology of stable minimal hypersurfaces in S^4 - Abstract

  Given an n-dimensional manifold (with n at least 4), it is generally impossible to control the topology of a homologically minimizing hypersurface M. In this talk, we construct stable (or locally minimizing) hypersurfaces with optimal restrictions on its topology in a 4-manifold X with natural curvature conditions (e.g. positive scalar curvature), provided that X admits certain embeddings into a homeomorphic S^4. As an application, we obtain black hole topology theorems in such 4-dimensional asymptotically flat manifolds with nonnegative scalar curvature. This is based on joint work with Boyu Zhang.

  
  

• Wednesday, September 17, 9:00-10:00, Zoom link (ID: 859 5741 3376, Code: 521730)
  Nicholas McCleerey (Purdue University) - Lines in the space of Kähler metrics - Abstract

  We report on joint work with Tamás Darvas, in which we establish a Ross-Witt Nyström correspondence for weak geodesic lines in the (completed) space of Kähler metrics. Using this, we construct a wide range of weak geodesic lines on any projective Kähler manifold which are not generated by holomorphic vector fields, thus disproving a folklore conjecture popularized by Berndtsson. Remarkably, some of these weak geodesic lines turn out to be smooth. In the case of Riemann surfaces, our results can be significantly sharpened. Finally, we investigate the validity of Euclid's fifth postulate for the space of Kähler metrics.

  
  

• Wednesday, October 8, 9:00-10:00, Zoom link (ID: TBA, Code: TBA)
  Yipeng Wang (Columbia University) - TBA - Abstract

  TBA

  
  

• Wednesday, October 15, 9:00-10:00, Zoom link (ID: TBA, Code: TBA)
  TBA (TBA) - TBA - Abstract

  TBA

  
  

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Schedule for the past years:

      2021-22 Fall       2021-22 Spring       2022-23 Fall       2022-23 Spring       2023-24 Fall       2023-24 Spring       2024-25 Fall       2024-25 Spring