Monday  

9:30 [talk 1] Yong Wei (USTC) 

Title: Curvature flows and Geometric inequalities. 

Abstract: I will review classical results on curvature flows of hypersurfaces and their applications in proving isoperimetric type inequalities. In particular, I will explain McCoy's proof of the Alexandrov-Fenchel inequalities for convex bodies in Euclidean space using mixed volume preserving curvature flows, as well as the extension by Guan and Li to star-shaped k-convex domains via inverse curvature flow.  

 

 

 

10:40 [talk 2] Jaehoon Lee (KIAS) 

Title: Minimal surfaces and the Weierstrass representation 

Abstract: The Weierstrass representation is a powerful tool for studying two-dimensional minimal surfaces in Euclidean space. It played a crucial role in the discoveries of Costa and Hoffman-Meeks, who constructed the first complete embedded minimal surfaces of arbitrary genus. As interest in high codimension minimal surfaces continues to grow, the Weierstrass representation is expected to continue playing an important role. In this talk, I will provide a basic introduction to minimal surfaces and the Weierstrass representation. 

 

 

 

19:00 [talk 3] Zhichao Wang (Fudan) 

Title: An introduction to Simon-Smith min-max theory

Abstract: In this talk, I will review the background of Almgren-Simon theory and Simon-Smith min-max theory. I will also present the outline of the proof of regularity.

 

 

20:10 [talk 4] Yohei Sakurai (Saitama) 

Title: Singularity analysis for Ricci flow 

Abstract: In the first talk, as an introduction, I review the singularity analysis for the Ricci flow including the classification of singularity models. 

 

 

 

 

Tuesday 

9:30 [talk 1] Yong Wei (USTC) 

Talk: Alexandrov-Fenchel inequalities in space forms. 

Abstract: I will present my joint work with Haizhong Li and Yingxiang Hu on the locally constrained inverse curvature flow (introduced by Brendle-Guan-Li 2018) in hyperbolic space. Using the tensor maximum principle, we prove that horo-convexity is preserved along the flow and that the solution converges smoothly to a geodesic sphere. As an application, we obtain a new proof of the Alexandrov-Fenchel inequalities for horo-convex domains in hyperbolic space. Furthermore, we establish new sharp geometric inequalities that compare integrals of Gauss–Bonnet curvatures with quermassintegrals. I will also briefly explain some other recent extensions, including analogous results on Alexandrov–Fenchel inequalities in the sphere and for hypersurfaces with capillary boundaries. 

 

 

 

10:40 [talk 2] Jiwoong Jang (Maryland) 

Title: Existence of flat flows for volume-preserving mean curvature flow with contact angle. 

Abstract: We present the motion as a weak solution of a droplet evolving by mean curvature with volume constraint and contact angle condition on a half space in this talk. Namely, we present the existence of a global-in-time weak solution, called the flat flow. A difficulty arises when we establish the local-in-time equi-boundedness of approximate solutions and a uniform L^2-estimate of multipliers. The difficulty is handled by conducting blowup analysis at a point in contact to a spherical cap with sharp angle. 

 

 

 

19:00 [talk 3] Zhichao Wang (Fudan) 

Title: Multiplicity one theorem for Simon-Smith min-max theory

Abstract: In this talk, I will present the multiplicity one theorem of Simon-Smith min-max theory. One of the main result is the min-max theory for prescribed mean curvature surfaces. This is a joint work with Xin Zhou.

 

  

 

20:10 [talk 4] Yohei Sakurai (Saitama) 

Title: Compactness theory for super Ricci flow 

Abstract: In the second talk, I discuss the compactness theory for super Ricci flow (super solution to the Ricci flow) established by Bamler (2021+, 2023). 

In particular, I explain the formulation of the metric flow and their F-convergence. 

 

 

 

 

Wednesday  

9:30 [talk 1] Yong Wei (USTC) 

Title : Volume preserving flows and Curvature measures. 

Abstract:  

The volume-preserving mean curvature flow in Euclidean space was introduced by Huisken (1987) and later extended to hyperbolic space by Cabezas-Rivas and Miquel (2007). It has been applied to prove isoperimetric type inequalities, and establish the existence of CMC foliations in asymptotically flat manifolds (Huisken and Yau). In this talk, I will present my work on volume preserving flows driven by powers of the k-th mean curvatures. Under suitable convexity assumptions, we analyze the convergence of such flows in both Euclidean and hyperbolic spaces. Key techniques in our proofs include the tensor/vector bundle maximum principle and curvature measure theory from convex geometry. The talk is based on joint work partly with Ben Andrews, Xuzhong Chen, Bo Yang, and Tailong Zhou. 

 

 

 

10:40 [talk 2] Tatsuya Miura (Kyoto) 

Title: Higher-order curvature flows for curves I: Introduction 

Abstract: In this series of talks we discuss higher-order (mainly fourth-order) curvature flows for curves in Euclidean space, including the surface diffusion flow and the elastic flow as typical examples. In the first part, we provide a brief introduction focusing on the case of closed curves, and we highlight the main differences from second-order flows, particularly those arising from the absence of maximum principles. 

 

 

 

 

Thursday 

9:30 [talk 1] Tatsuya Miura (Kyoto) 

Title: Higher-order curvature flows for curves II: Long-time behavior 

Abstract: In the second part of this talk, we continue the discussion of higher-order flows for closed curves. Going into the details of Dziuk--Kuwert--Schätzle-type energy methods, we examine the long-time behavior of solutions, and in particular discuss Escher--Ito's problem with its extensions. 

 

 

 

 

10:40 [talk 2] Eungbeom Yeon (Pusan) 

Title: Complete Embedded Minimal Surfaces of Finite Topology in Euclidean Spaces 

Abstract: In 1983, Costa discovered a complete embedded minimal surface in three-dimensional Euclidean space with genus one and three embedded ends. Building on this result, Hoffman and Meeks later constructed complete embedded minimal surfaces with three embedded ends and arbitrary genus. These surfaces can be viewed as desingularizations of the union of a catenoid and a plane along their intersection circle. In this talk, we aim to explore analogous constructions in four- and five-dimensional Euclidean spaces. Specifically, we discuss the desingularizations of the union of a Lagrangian catenoid with a two-dimensional plane and of a Hoffman–Osserman catenoid with a two-dimensional plane, highlighting both the similarities and the differences from the Costa–Hoffman–Meeks surfaces in three-dimensional space. 

 

 

 

19:00 [talk 3] Tatsuya Miura (Kyoto) 

Title: Higher-order curvature flows for curves III: Non-compact case 

Abstract: In the third part of this talk, we present our recent joint work with Fabian Rupp (University of Vienna) on extending the above energy methods from compact to non-compact curves. 

  

 

 

20:10 [talk 4] Yohei Sakurai (Saitama) 

Title: Almost splitting for super Ricci flow. 

Abstract: In the final talk, I will talk about almost splitting and quantitative stratification results for super Ricci flow. 

First, I describe our setting so-called ``D-condition” introduced by Buzano (2010), and also a recent development by Flaim-Hupp (2025+) for its geometric interpretation and optimal transport characterization. 

After that, I present the main result obtained in the joint work with Keita Kunikawa (Tokushima university). 

 

 

 

Friday 

9:30 [talk 1]  Zhichao Wang (Fudan) 

Title: Minimal spheres and tori in three-spheres

Abstract: In this talk, we introduce the progress in constructing minimal spheres and tori in spheres. In particular, we prove that for a generic metric or positive Ricci curvature metric on S^3, there are at least four minimal spheres; if a generic metric has positive Ricci curvature, then there are at least 9 embedded minimal tori. This is based on a joint work with Xin Zhou and another work with Xingzhe Li.

 

 

10:20 [talk 2] Jooho Lee (KIAS) 

Title: An introduction to special lagrangian geometry 

Abstract: Special Lagrangian submanifolds form a distinguished class of calibrated, volume-minimizing objects in Calabi–Yau manifolds, linking symplectic geometry, complex geometry, and geometric analysis. Their singularities are often modeled by special Lagrangian cones, which provide natural examples of area-minimizing cones in higher dimensions. This talk introduces the basic geometry of special Lagrangians.