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: Closed-strings mirror symmetry for semiprojective toric manifolds

Abstract: In this talk, I will review recent joint work with Alexander Ritter on semiprojective toric manifolds. These are non-compact toric manifolds, defined as GIT/Kahler quotients of torus actions on a vector spaces, and as such, are symplectic C*-manifolds, defined in our previous work. 

As a particular instance of that work, the quantum and symplectic cohomology of these toric manifolds are well defined, moreover we can compute them explicitly. We prove that symplectic cohomology of a semiprojective toric manifold is isomorphic to the Jacobian ring of its superpotential, thereby establishing the closed-string mirror symmetry statement for these manifolds.

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

Speaker: Catherine Cannizzo (Columbia) 

Title: Wrapping Lagrangians in the Fukaya category of a symplectic fibration

Abstract: Mirror symmetry is a string-theory inspired duality between manifolds: given a manifold X, what is its mirror Y? The aim of the conjectured algebraic version is to leverage this duality between two branches of geometry, the complex geometry on X and the symplectic geometry on Y. This exploration depends on the curvature of X, which significantly impacts the mirror Y. Originally studied between compact dual Calabi-Yau manifolds (zero first Chern class), recent work focuses on mirrors to Fano (positive first Chern class) and general type (such as negative first Chern class). 

The Fukaya category is the algebraic invariant of symplectic manifolds in the homological mirror symmetry conjecture. Lagrangian submanifolds are objects, and their intersections are morphisms. Mirrors to Fano and general type impose conditions on how non-compact Lagrangian ends can wrap. We prove a new homological mirror symmetry result between complex line bundles on a blow-up of a four-torus times C, and Lagrangians which wrap around a puncture on the symplectic manifold in the Fukaya category. We view the symplectic side as a symplectic fibration. This is joint work with Sara Venkatesh in arXiv:2508.06379.

Monday 4/20/26 (In-person, CU 216, 4:00 PM)

Speaker: Or Hershkovits (University of Maryland) 

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: On the Rate of Convergence of Cylindrical Singularity in Mean Curvature Flow

Abstract: We prove that if a rescaled mean curvature flow is a global graph over the round cylinder with small gradient and converges at a super-exponential rate, then it must coincide with the cylinder itself. We also show that this result is sharp by constructing local graphical counterexamples with arbitrarily fast super-exponential convergence on rapidly expanding domains. These examples form infinite-dimensional families of Tikhonov-type solutions and show that unique continuation fails for local graphical solutions. Our constructions apply to a broad class of nonlinear equations. This talk is based on work of Yiqi Huang and Xinrui Zhao.