Peking-Westlake Geometric Analysis Seminar (Spring 2025)

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

  • Tencent Meeting: 409 9581 4561 Password: 583483 .
  • Zoom: TBA (see below) .
  • The schedule is shown in the following table and you can find the details of the planned talks below this table.

    Week 1 (Feb 19, 9-10:30AM) Week 2 (Feb 26, 9-10:30AM) Week 3 (Mar 5, 9-10:30AM) Week 4 (Mar 12, 9-10:30AM)
    Speaker: Speaker: Prof. Hongzhi Huang (黄虹智) Speaker: Speaker: Prof. Xiaoshang Jin (靳晓尚)
    Week 5 (Mar 19, 9-10:30AM) Week 6 (Mar 26, 9-10:30AM) Week 7 (Apr 2, 9-10:30AM) Week 8 (Apr 9, 9-10:30AM)
    Speaker: Prof. Gang Li (李刚) Speaker: Dr. Ziyi Zhao (赵子颐) Speaker: Dr. Shuli Chen (陈淑漓) Speaker: Dr. Shihang He (何世航)
    Week 9 (Apr 16, 9-10:30AM) Week 10 (Apr 23, 2-3:30PM) Week 11 (Apr 30, 9-10:30AM) Week 12 (May 7, 3-4PM)
    Speaker: Prof. Tongrui Wang (王童瑞) Speaker: Prof. Fang Wang (王芳) Speaker: Dr. Yipeng Wang Speaker: Dr. Reiser Philipp
    Week 13 (May 14, 9-10:30AM) Week 14 (May 21, 9-10:30AM) Week 15 (May 28, 9-10:30AM) Week 16 (Jun 4, 9-10:30AM)
    Speaker: Dr. Kai Xu (徐恺) Speaker: Dr. Junrong Yan (颜俊榕) Speaker: Prof. Yiyue Zhang (张一岳) Speaker:
    Week 17 (Jun 11, 9-10:30AM) Week 18 (Jun 18, 9-10:30AM)
    Speaker: Speaker:

    Previous Seminars

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


    1. 2025 Feb 19, 9-10:30 AM,
    Tencent Meeting

    Speaker:

    Title:
    Abstract:

    2. 2025 Feb 26, 9-10:30 AM,
    Tencent Meeting: 409 9581 4561 Password: 583483 .

    Speaker: Prof. Hongzhi Huang (Jinan University)

    Title: Nonnegative Ricci Curvature, Euclidean Volume Growth, and the Fundamental Groups of Open $4$-Manifolds
    Abstract: Let $M$ be a $4$-dimensional open manifold with nonnegative Ricci curvature. We prove that if the universal cover of $M$ has Euclidean volume growth, then the fundamental group is finitely generated and contains an abelian subgroup whose index is bounded by a universal contant. This is joint work with Xian-Tao Huang.

    3. 2025 Mar 5, 9-10:30 AM,
    Tencent Meeting


    Title:
    Abstract:

    4. 2025 Mar 12, 9-10:30 AM,
    Tencent Meeting: 409 9581 4561 Password: 583483 .

    Speaker: Prof. Xiaoshang Jin (HUST)

    Title: Sharply Estimating Hyperbolic Capacities
    Abstract: In this talk, we will introduce the four types of sharp capacitary inequalities within the hyperbolic space. It is a joint work with professor Jie Xiao (MUN).

    5. 2025 Mar 19, 9-10:30 AM,
    Tencent Meeting: 409 9581 4561 Password: 583483 .

    Speaker: Prof. Gang Li (Shandong University)

    Title: A normalized Ricci flow on compact 2-D surfaces with boundary towards the complete hyperbolic metric in the interior.
    Abstract: We consider the initial-boundary value problem of the normalized Ricci flow on a given compact 2-D surfaces with boundary, with prescribed geodesic curvature on the boundary. We establish a large class of initial-boundary data, so that the flow exists for all $t>0$, and converges locally uniformly to the complete hyperbolic metric in the interior of the surface.

    6. 2025 Mar 26, 9-10:30 AM,
    Tencent Meeting: 409 9581 4561 Password: 583483 .

    Speaker: Dr. Ziyi Zhao (Westlake University)

    Title: Wulff inequality for minimal submanifolds in Euclidean space
    Abstract: Geometric inequality for minimal submanifolds in Euclidean space plays very important role in geometric analysis. In this talk, we will talk about recent work, that we prove a Wulff inequality for $n$-dimensional minimal submanifolds with boundary in $R^{n+m}$, where we associate a nonnegative anisotropic weight to the boundary of minimal submanifolds. The Wulff inequality constant depends only on $m$ and $n$, and is independent of the weights. The inequality is sharp if $m = 1, 2$ and the weight is the support function of ellipsoids or certain type of centrally symmetric long convex bodies. This is a joint work with Wenkui Du and Yuchao Yi.

    7. 2025 Apr 2, 9-10:30 AM,
    Zoom: 989 6488 6047 Password: 213908 .

    Speaker: Dr. Shuli Chen (UChicago)

    Title: Interior control for surfaces with positive scalar curvature and its application
    Abstract: Let $M^{n}$, $n\in\{3,4,5\}$, be a closed aspherical $n$-manifold and $S\subset M$ a subset consisting of disjoint incompressible embedded closed aspherical submanifolds (possibly with different dimensions). When $n =3,4$, we show that $M\setminus S$ cannot admit any complete metric with positive scalar curvature. The key ingredient is a new interior control for the extrinsic diameter of surfaces with positive scalar curvature. This is joint work with Jianchun Chu (Peking University) and Jintian Zhu (Westlake University).

    8. 2025 Apr 9, 9-10:30 AM,
    Tencent Meeting: 409 9581 4561 Password: 583483 .

    Speaker: Dr. Shihang He (Peking University)

    Title: Positive mass theorems on singular spaces and some applications
    Abstract: We establish positive mass theorems on singular spaces under the assumption that the scalar curvature is nonnegative in the strong spectral sense. As an application, we obtain desingularization results for strongly stable minimal hypersurfaces in asymptotically flat (AF) 8-manifolds. These results reveal certain positive effect of the minimal hypersurface singularities in scalar curvature geometry, which also leads to an alternative proof of the positive mass theorem in dimension 8. This is joint work with Professors Yuguang Shi and Haobin Yu.

    9. 2025 Apr 16, 9-10:30 AM,
    Tencent Meeting: 409 9581 4561 Password: 583483 .

    Speaker: Prof. Tongrui Wang (SJTU)

    Title: On the topology of manifolds with positive intermediate curvature
    Abstract: In this talk, I will introduce a conjecture relating the topology of a manifold's universal cover with the existence of metrics with positive m-intermediate curvature. We prove the result in dimension 3~5 and for most choices of m in dimension 6. As a corollary, we show that a closed aspherical 6-manifold cannot admit a metric with positive 4-intermediate curvature. This talk is base on the joint work with Liam Mazurowski and Xuan Yao.

    10. 2025 Apr 23, 2-3:30 PM,
    Tencent Meeting: 409 9581 4561 Password: 583483 .

    Speaker: Fang Wang (SJTU)

    Title: Rigidity Theorem for Poincare-Einstein Manifolds
    Abstract: In this talk, I first introduce the classical rigidity theorem for Poincare-Einstein manifold, which has conformal compactification in high regularity. Then I will report some recent rigidity result for Poincare-Einstein manifold in the upper half plane model, which take the Euclidean space as its conformal infinity and whose adapted conformal metric has quadratic curvature decay at infinity. This is joint work with Sanghoon Lee (KIAS).

    11. 2025 Apr 30, 9-10:30 AM,
    Zoom: 989 6488 6047 Password: 213908 .

    Speaker: Dr. Yipeng Wang (Columbia University)

    Title: Rigidity Results Involving Stabilized Scalar Curvature
    Abstract: Gromov introduced the notion of stabilized scalar curvature, which arises naturally in the context of warped product extensions. This concept also appears in the study of the geometry of weighted manifolds and in Perelman's work on the Ricci flow. In this talk, I will explore the relationship between various formulations of stabilized scalar curvature and explain how several classical scalar curvature rigidity results can be extended to this more general setting.

    12. 2025 May 7, 3-4 PM,
    Zoom: 989 6488 6047 Password: 213908 .

    Speaker: Philipp Reiser (University of Fribourg)

    Title: Manifolds of positive Bakry-Emery Ricci curvature
    Abstract: The Bakry-Emery Ricci tensor is a generalization of the classical Ricci tensor to the setting of weighted Riemannian manifolds, i.e. Riemannian manifolds whose Riemannian volume forms are weighted by a smooth function. In analogy with important open problems in the Riemannian case, we consider the question of which manifolds admit a weighted Riemannian metric of positive Bakry-Emery Ricci curvature. We will show that surgery techniques that are used in the Riemannian case can be extended and improved in the weighted case. As application we will construct weighted Riemannian metrics of positive Bakry-Emery Ricci curvature on all closed, simply-connected spin 5-manifolds. This is joint work with Francesca Tripaldi.

    13. 2025 May 14, 9-10:30 AM,
    Zoom: 989 6488 6047 Password: 213908 .

    Speaker: Kai Xu (Duke University)

    Title: $3$-Manifolds with positive scalar curvature and bounded geometry
    Abstract: In this talk we will work towards proving the following theorem: a contractible $3$-manifold with positive scalar curvature and bounded geometry must be diffeomorphic to $R^3$. The proof involves running an innermost weak inverse mean curvature flow on the manifold. This talk is based on joint work with Otis Chodosh and Yi Lai.

    14. 2025 May 21, 9-10:30 AM,
    Zoom: 989 6488 6047 Password: 213908 .

    Speaker: Junrong Yan (Northeastern University)

    Title: Heat Kernel Expansion and Weyl's Law for Schrodinger-Type Operators on Noncompact Manifolds
    Abstract: Motivated by the study of Landau-Ginzburg models in string theory from the viewpoint of index theorem, we explore the heat kernel expansion for Schrodinger-type operators on noncompact manifolds. This expansion leads to a local index theorem for such operators. Unlike in the compact case, the heat kernel in the noncompact setting exhibits new behaviors. Obtaining its precise expansion and deriving a remainder estimate require careful analysis. We will first present our approach to establishing this expansion. As a key application, we study Weyl's law for such operators. In the compact case, such results follow from Karamata's Tauberian theorem, but the standard Tauberian argument does not apply in the noncompact setting. To address this, we develop a new version of Karamata's theorem. This is joint work with Xianzhe Dai.

    15. 2025 May 28, 9-10:30 AM,
    Tencent Meeting: 409 9581 4561 Password: 583483 .

    Speaker: Yiyue Zhang (BIMSA)

    Title: Rigidity of the Positive Mass Theorems
    Abstract: Schoen-Yau and Witten demonstrated that the total mass $m$ of asymptotically flat initial data sets(IDS) in general relativity are non-negative. Combining spinorial methods with spacetime harmonic functions, we prove that if $m=0$, the IDS must embed into a pp-wave spacetime. This resolves the rigidity conjecture for the spacetime positive mass theorem on spin manifolds in all dimensions. Furthermore, adapting these techniques to the hyperboloidal setting, we establish that asymptotically hyperboloidal IDS with zero mass must embed isometrically into Minkowski space, contrasting with the asymptotically flat case. It is joint work with Sven Hirsch and Hyun Chul Jang.

    16. 2025 Jun 4, 9-10:30 AM,
    Tencent Meeting


    Title:
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    17. 2025 Jun 11, 9-10:30 AM,
    Tencent Meeting


    Title:
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    18. 2025 Jun 18, 9-10:30 AM,
    Tencent Meeting