Peking-Westlake Geometric Analysis Seminar (Spring 2026)

This is a Geometric Analysis Seminar held by

  • Prof. Yuguang Shi (Peking University)
  • and Dr. Jintian Zhu (Westlake University).

    • We welcome everyone who is interested in attending our seminar. If you would like to be added in the email list, please tell us by sending an email to zhujintian AT westlake DOT edu DOT cn or haotz AT pku DOT edu DOT cn.

    Our seminar usually lasts 1.5 hours (including one-hour talk and half-hour discussion) but it would be flexible according to the speaker. The seminar will be arranged at

  • (Morning Session) 9:00-10:30 AM, every Thursday (Beijing time).

    • The talk will be given online with Tencent Meeting or Zoom (optional if the speaker cannot use Tencent Meeting).

  • Tencent Meeting: 457-6962-6473 Password: 7374 .

    • The schedule is shown in the following table and you can find the details of the planned talks below this table.

    Week 1 (Mar 5, 9-10:30AM) Week 2 (Mar 12, 9-10:30AM) Week 3 (Mar 19, 9-10:30AM) Week 4 (Mar 26, 9-10:30AM)
    Speaker: Speaker: Xuan Yao Speaker: Speaker:
    Week 5 (Apr 2, 9-10:30AM) Week 6 (Apr 7, 14-15:30PM) Week 7 (Apr 16, 9-10:30AM) Week 8 (Apr 23, 9-10:30AM)
    Speaker: Speaker: Yukai Sun Speaker: Speaker:
    Week 9 (Apr 30, 9-10:30AM) Week 10 (May 7, 9-10:30AM) Week 11 (May 14, 9-10:30AM) Week 12 (May 21, 9-10:30AM)
    Speaker: Speaker: Speaker: Yipeng Wang Speaker: Jingche Chen
    Week 13 (May 28, 9-10:30AM) Week 14 (June 4, 9-10:30AM) Week 15 (June 11, 9-10:30AM) Week 16 (June 18, 9-10:30AM)
    Speaker: Yuanyuan Li Speaker: Yiyue Zhang Speaker: Guodong Wei Speaker: Conghan Dong

    Previous Seminars

  • Spring 2023
  • Autumn 2023
  • Spring 2024
  • Autumn 2024
  • Spring 2025
  • Autumn 2025

    • Autumn 2025


    Week 1 (Morning)
    Tencent Meeting: 457-6962-6473 Password: 7374 .

    Speaker: Xuan Yao (Princeton University)

    Title: Capillary minimal slicing and scalar curvature rigidity in dimension $4$
    Abstract: We develop a capillary minimal slicing technique and as a result, we prove a scalar curvature rigidity result in dimension $4$.

    Week 6 (Afternoon)
    Tencent Meeting: 457-6962-6473 Password: 7374 .

    Speaker: Sun Yukai (Henan University)

    Title: Warped area-minimizing hypersurface and warped product metric
    Abstract: We first review the related conclusions about the splitting into product metric for area-minimizing hypersurfaces under some proper conditions. Then we discuss the basic knowledge of warped area-minimizing hypersurfaces. At last, we can prove that the metric is locally splitting into a warped product metric under the condition of spectral curvature.

    Week 11 (Morning)
    Tencent Meeting: 457-6962-6473 Password: 7374 .

    Speaker: Yipeng Wang

    Title: The Positive Mass Theorem in Arbitrary Dimensions
    Abstract: We present an inductive scheme for proving the positive mass theorem in arbitrary dimensions, extending the Schoen–Yau argument from dimensions at most 7 to the general case. This is a joint work with Simon Brendle.

    Week 12 (Morning)
    Tencent Meeting: 457-6962-6473 Password: 7374 .

    Speaker: Jingche Chen

    Title: Homological (n-2)-systole in n-manifold with positive tri-Ricci curvature.
    Abstract: We first review the related conclusions about systole inequality under positive curvature condition. Then we discuss the basic knowledge of intermediate curvature and weighted minimal slicing introduced by Brendle-Hirsch-Johne. Finally, we present our results about homological (n-2)-systole inequality under positive tri-Ricci curvature condition. If time permits, I will show some ideas of the recent development about k-systole inequality which connects with the Zhu and Chu-Lee-Zhu' results. This is a joint work with Han Hong.

    Week 13 (Morning)
    Tencent Meeting: 457-6962-6473 Password: 7374 .

    Speaker: Yuanyuan Li

    Title: The Mahler conjecture in dimension three
    Abstract: We settle the three-dimensional Mahler conjecture for arbitrary convex bodies. Prior to this work, the Mahler conjecture for arbitrary convex bodies had remained open in all dimensions \(n\geq 3\) since Mahler's original work in 1938. More precisely, for every convex body \(K\subset \mathbb R^3\), we prove the sharp inequality \[|K|\, |K^{s(K)}|\geq \frac{64}{9},\] where \(K^{s(K)}\) denotes the polar of \(K\) with respect to Santal\'o point \(s(K)\). The lower bound is attained by simplices; among polytopes, these are the only equality cases. The key ingredient in our proof is an admissible shadow-system framework, which produces face-lattice-preserving, volume-affine deformations and reduces the problem to a dimension count for the space of admissible speeds. As an application, this framework also yields a purely geometric new proof of the three-dimensional centrally symmetric Mahler inequality, first proved by Iriyeh and Shibata. This is joint work with Shibing Chen (USTC)，Dongmeng Xi(SHU) and Zhe-Feng Xu(SISSA&USTC).

    Week 14 (Morning)
    Tencent Meeting: 457-6962-6473 Password: 7374 .

    Speaker: Yiyue Zhang

    Title: The hyperboloidal positive mass theorem
    Abstract: Building on the recent work of Brendle–Wang on the Riemannian positive mass theorem, together with the Jang equation techniques developed by Schoen–Yau, Sakovich, and Lundberg, we prove the spacetime positive mass theorem for asymptotically hyperboloidal initial data sets in arbitrary dimensions. This is joint work with Hirsch, Khuri, and Lesourd. Additionally, I will discuss several rigidity results in the asymptotically hyperbolic setting.

    Week 15 (Morning)
    Tencent Meeting: 457-6962-6473 Password: 7374 .

    Speaker: Guodong Wei

    Title: Surgery and total mean curvature
    Abstract: In this talk, I will discuss the main ideas of the paper by Frenck, Hanke, and Hirsch; see arXiv:2601.10617.