In the 2026 Spring semester, the seminars will be held both online and in-person (CU 216).  Online talks are usually on Thursdays starting at 4:30 PM, and in-person talks will be on Mondays at 4:00 PM.

Organizers: Huai-Dong Cao, Andrew Harder, Ao Sun, Xiaofeng Sun.

If you are interested in participating in the seminar, please email Ao (aos223 at lehigh dot edu).

Monday 2/9/26 (In-person, CU 216, 4:00 PM)

Speaker: Qi Sun (Wisconsin-Madison) 

Title: Singularities of Curve Shortening Flow with Convex Projections

Abstract: Understanding singularity formation is an important topic in the study of geometric flows. Since Gage-Hamilton-Grayson’s foundational results, it has largely been unknown how singularities of curve shortening flow form in higher codimensions. In this talk, I will present my recent results that in n dim Euclidean space, any curve with a one-to-one convex projection onto some 2-plane develops a Type I singularity and becomes asymptotically circular under curve shortening flow. As a corollary, an analog of Huisken's conjecture for curve shortening flow is confirmed, in the sense that any closed immersed curve in n dim Euclidean space can be perturbed in n+2 dim Euclidean space to a closed immersed curve which shrinks to a round point under curve shortening flow.

Monday 3/2/26 (In-person, CU 216, 4:00 PM)

Speaker: Alex Mramor (University of Oklahoma) 

Title: On an ancient stacked pancake solution to mean curvature flow

Abstract: In this talk, after giving a brief survey of some ancient solutions and their importance in the mean curvature flow, I’ll discuss a recent collaboration with Mat Langford (ANU) and Louis Yudowitz (KTH) on the construction of a new solution to MCF by “stacking” two ancient pancakes.

Monday 3/16/26 (In-person, CU 216, 4:00 PM)

Speaker: Junming Xie (Rutgers) 

Title: Hamilton–Ivey-type curvature pinching of Ricci solitons

Abstract: A remarkable feature of the three-dimensional Ricci flow is the classical Hamilton–Ivey curvature pinching estimate. Roughly speaking, it asserts that when curvature blows up along the 3D Ricci flow, the positive curvature must blow up at a faster rate than the absolute value of the negative curvature. As a consequence, any 3D shrinking or steady gradient Ricci soliton (or more generally, any ancient solution) arising as a limit of parabolic blow-ups necessarily has nonnegative sectional curvature. This fact plays a central role in the analysis of 3D singularity models, as it enables the effective use of the Li–Yau–Hamilton differential Harnack inequality and the structure theory of nonnegatively curved three-manifolds. 

In recent years, various generalizations of the Hamilton–Ivey curvature pinching estimate have been obtained for shrinking and steady Ricci solitons, more broadly for ancient solutions, and in higher dimensions. In this talk, based on joint work with Huai-Dong Cao, we will discuss some recent developments on Hamilton–Ivey-type curvature pinching estimates for gradient Ricci solitons, including newly discovered estimates for asymptotically conical expanding solitons.

Monday 3/23/26 (In-person, CU 216, 4:00 PM)

Speaker: Hanbing Fang (Stony Brook) 

Title: Strong uniqueness of tangent flows at cylindrical singularities in Ricci flow

Abstract: The uniqueness of tangent flows is central to understanding singularity formation in geometric flows. A foundational result of Colding and Minicozzi establishes this uniqueness at cylindrical singularities under the Type I assumption in the Ricci flow. In this talk, I will present a strong uniqueness result for cylindrical tangent flows at the first singular time. Our proof hinges on a Łojasiewicz inequality for the pointed $\mathcal{W}$-entropy, which is established under the assumption that the local geometry near the base point is close to a standard cylinder or its quotient. This is joint work with Yu Li.

Monday 3/30/26 (In-person, CU 216, 4:00 PM)

Speaker: Filip Zivanovic (Simons Center for Geometry and Physics) 

Title: TBD

Abstract: TBD

Monday 4/6/26 (In-person, CU 216, 4:00 PM)

Speaker: Catherine Cannizzo (Columbia) 

Title: TBD

Abstract: TBD

Monday 4/27/26 (In-person,  CU 216, 4:00 PM, special seminars)

Speaker: Yiqi Huang (MIT) and Xinrui Zhao (Yale) 

Title: TBD

Abstract: TBD