6th Geometry Day

Date: 2026. 10. 02. Friday

Location: Room 414, Continuing Education Building, Sookmyung Women's University

Schedule

• 01:20 - 01:50 : [Opening Talk] Seungsu Hwang (Chung-Ang University)

• 01:50 - 02:00  :  (Break time)

• 02:00 - 02:20 :  Jihyeon Lee (IBS-CGP)

• 02:25 - 02:45 :  Jooyeon Park (Sookmyung Women's University)

• 02:45 - 03:00  :  (Break time)

• 03:00 - 03:20 :  Kyeongho Bang (KAIST)

• 03:25 - 03:45 :  Kiyoon Eum (KAIST) 

• 03:50 - 04:10 :  Junyoung Kim (KAIST) 

• 04:10 - 04:25  :  (Break time)

• 04:25 - 04:45 :  Seunghoon Jeong (Postech)

• 04:50 - 05:10 :  Jungwoo Moon (Chung-Ang University)

Title & Abstract

• Seungsu Hwang (Chung-Ang University)

Title : Besse conjecture 

Abstract:  On a compact $n$-dimensional manifold $M$, a critical point of the total scalar curvature, restricted to the space of metrics with constant scalar curvature of unit volume, satisfies the critical point equation (CPE), given by $z_g=s_g'^*(f)$. Besse conjecture says that a solution $(g,f)$ of the CPE is Einstein. In this talk, we will review what is currently known about this conjecture and related topics.

• Jihyeon Lee (IBS-CGP)

Title : Rigidity of Hamiltonian Minimal Twisted Tori in $\mathbb{CP}^n$ 

Abstract:  Twisted tori form a natural class of Lagrangian submanifolds in $\mathbb{CP}^n$ whose geometry is determined by a single planar profile curve. In this talk, we study the Hamiltonian minimal condition for twisted tori, and derive an explicit ordinary differential equation for the generating curve. Using this reduction, we prove a rigidity result: under a geometric condition relating the radial function and the mean curvature, a Hamiltonian minimal twisted torus must be a toric product torus. In particular, no Chekanov-type twisted torus satisfying this condition can be Hamiltonian minimal. Finally, we briefly discuss the possibility of non-product Hamiltonian minimal twisted tori in $\mathbb{CP}^n$ and present numerical evidence for Chekanov-type candidates.

•  Jooyeon Park (Sookmyung Women's University)

Title : Rigidity of free boundary hypersurfaces with constant higher order mean curvature in a convex cone of a warped product space

Abstract:  We study rigidity of compact free boundary hypersurfaces with constant higher order mean curvature in convex cones of warped product spaces. Under suitable geometric assumptions on the ambient warped product space, we prove that any embedded, star-shaped, and convex free boundary hypersurface with constant $l$-th order mean curvature, $1\le l\le n$, must be umbilic. This is joint work with Keomkyo Seo.

• Kyeongho Bang (KAIST)

Title : Ancient Ricci flow in dimension 2 

Abstract: We establish the existence and uniqueness modulo time-independent diffeomorphisms of the positively curved ancient Ricci flow (M^2, g(t)) on a two-dimensional compact connected surface with boundary, assuming constant positive boundary geodesic curvature. To our knowledge, this result is the first instance of a classification result for ancient Ricci flows with boundary. 

• Kiyoon Eum (KAIST) 

Title : Geometry of the fractional quantum Hall effect 

Abstract:  The fractional quantum Hall effect is an important physical phenomenon that has played a central role in our understanding of topological phases of matter. In this talk, I will introduce this phenomenon, emphasizing how geometry encodes its physical properties.   

• Junyoung Kim (KAIST) 

Title : Rigidity and volume pinching for the sharp gradient estimate in positive Ricci curvature 

Abstract: Colding established a sharp gradient estimate for the Green function on manifolds with nonnegative Ricci curvature, which was extended to positive Ricci curvature by Manea recently. In this talk, we discuss the quantitative volume pinching, the almost rigidity for manifolds with Ricci lower bound and the rigidity for closed Einstein manifolds of this sharp gradient esitmate. If time permits, we will present a rigidity theorem for closed Einstein 4-manifolds, whose proof relies on a new monotonicity formula. This is joint work with Jiewon Park. 

• Seunghoon Jeong (Postech)

Title : Thom’s gradient conjecture and its applications 

Abstract: In geometric analysis, Łojasiewicz-type inequalities provide a powerful framework for studying the asymptotic behavior of gradient flows near critical points.  This theory, originating from Łojasiewicz’s work in the 1960s and Simon’s infinite-dimensional extension in 1983, also encompasses questions such as Thom’s gradient conjecture conjecture on the asymptotic direction of analytic gradient trajectories. In this talk, we begin with Łojasiewicz theory and its applications to gradient-like geometric PDEs, and then discuss recent developments concerning Thom’s gradient conjecture, with a focus on its applications to optimal transport.

• Jungwoo Moon (Chung-Ang University)

Title : Some properties of adjusted Ricci curvature on compact foliated manifolds

Abstract: In this talk, we study the definition of the adjusted Ricci curvature of a Riemannian foliation on compact manifolds to reinforce the comprehension of transverse Ricci curvature. Specifically, we compare the basic properties of the adjusted Ricci curvature with the properties of both Ricci curvature and transverse Ricci curvature.