http://www-math.umd.edu/research/seminars.html http://www-math.umd.edu/research/seminars.html Tue, 21 Oct 2025 15:30:00 EDT Where: Kirwan Hall 1313
Speaker: Carlos Esparza (Berkeley) - https://math.berkeley.edu/~esparza/
Abstract: We show that, up to biholomorphism, a given noncompact complex manifold admits at most one shrinking gradient Kähler-Ricci soliton with Ricci curvature vanishing at infinity. Time permitting, we will also discuss how the technique for proving the uniqueness of the soliton vector field can be applied to other settings, such as AC Calabi-Yau manifolds.
]]> http://www-math.umd.edu/research/seminars.html Tue, 04 Nov 2025 15:30:00 EST Where: Kirwan Hall 1313
Speaker: Ao Sun (Lehigh) - https://sites.google.com/view/aosun/
Abstract: The cylindrical singularities are prevalent but complicated in geometric flows. We discuss one of the simplest extrinsic flow, the mean curvature flow, and illustrate how the local dynamics of the singularities influence the singular set itself, and the geometry and topology of the flow. This talk is based on joint works with Zhihan Wang (Cornell) and Jinxin Xue (Tsinghua).
]]> http://www-math.umd.edu/research/seminars.html Tue, 11 Nov 2025 15:30:00 EST Where: Kirwan Hall 1313
Speaker: Yueqiao Wu (JHU) - https://sites.google.com/view/yueqiaow/
Abstract: The question of finding and classifying complete Calabi--Yau metrics on smooth affine varieties of Euclidean volume growth goes back to Tian--Yau, who constructed such metrics on X given by the complement of a Kähler--Einstein divisor in a Fano variety. Recent classification results suggest that such metrics on smooth affine varieties come from prescribing the asymptotic geometry using a negative valuation. In this talk, I will revisit Tian--Yau's example, in which case the Kähler--Einstein divisor defines a K-semistable valuation which does not admit a center on X. Generalizing this leads to a valuative criterion for K-semistable valuations at infinity on a given affine variety. Time permitting, I will also explain that these valuations in fact come from Fano type compactifications generalizing the Tian--Yau case. This is based on joint work in progress with Mattias Jonsson.
]]> http://www-math.umd.edu/research/seminars.html Tue, 18 Nov 2025 15:30:00 EST Where: Kirwan Hall 1313
Speaker: Benjy Firester (MIT) - https://benjyjf.com/
Abstract: In this talk, I will present a variational framework to solve a general class of free-boundary Monge–Ampère equations. This approach combines the classical first and second boundary value problems by imposing both the boundary data and the gradient image of the solution. I will explore applications to the Monge–Ampère eigenvalue problem and a reconstruction theorems, and geometric problems including a hemispherical Minkowski problem, Calabi-Yau metrics, and free boundary toric Kähler–Einstein/Kähler-Ricci soliton metrics. Furthermore, I will discuss the connection to the boundary regularity of optimal transport and recent progress inspired by geometric regularity theory techniques.
]]> http://www-math.umd.edu/research/seminars.html Tue, 02 Dec 2025 15:30:00 EST Where: Kirwan Hall 1313
Speaker: Tamas Darvas (UMD) -
Abstract: Given a compact Kähler manifold, to better understand Mabuchi's K energy we introduce a family of K^beta energies, whose favorable properties are similar to those of the Ding energy from the Fano case. The construction uses Berman's transcendental quantization, and we show that the slope of the K^beta energies along test configurations can be computed using intersection theory. With these ingredients in place we provide a uniform Yau-Tian-Donaldson correspondence that characterizes the existence of a unique constant scalar curvature Kähler metric using test configurations. Combining our techniques with the non-Archimedean approach to K-stability pioneered by Boucksom-Jonsson, we show that the properness of the classical energy can be tested by checking its slope along a distinguished subclass of Li-type models, called log discrepancy models, thus yielding another G-uniform Yau--Tian--Donaldson correspondence. (Joint with Kewei Zhang)
]]> http://www-math.umd.edu/research/seminars.html Tue, 09 Dec 2025 15:30:00 EST Where: Kirwan Hall 1313
Speaker: Tang-Kai Lee (Columbia) -
Abstract: The smooth mean curvature flow often develops singularities, making weak solutions essential for extending the flow beyond singular times, as well as having applications for geometry and topology. Among various weak formulations, the level set flow method is notable for ensuring long-time existence and uniqueness. However, this comes at the cost of potential fattening, which reflects genuine non-uniqueness of the flow after singular times. Even for flows starting from smooth, embedded, closed initial data, such non-uniqueness can occur. Thus, we can't expect genuine uniqueness in general. Addressing this non-uniqueness issue is a difficult problem. With Alec Payne, we establish an intersection principle comparing two intersecting flows. We prove that level set flows satisfy this principle in the absence of non-uniqueness.
]]> http://www-math.umd.edu/research/seminars.html Thu, 19 Feb 2026 12:30:00 EST Where: Kirwan Hall 3206
Speaker: Richard Bamler (Berkeley) -
Abstract: We resolve the Mean Convex Neighborhood Conjecture for mean curvature flows in all dimensions and for all types of cylindrical singularities. Specifically, we show that if the tangent flow at a singular point is a multiplicity-one cylinder, then in a neighborhood of that point the flow is mean-convex, its time-slices arise as level sets of a continuous function, and all nearby tangent flows are cylindrical. Moreover, we establish a canonical neighborhood theorem near such points, which characterizes the flow via local models. Our proof relies on a complete classification of ancient, asymptotically cylindrical flows. We prove that any such flow is non-collapsed, convex, rotationally symmetric, and belongs to one of three canonical families: ancient ovals, the bowl soliton, or the flying wing translating solitons. Our approach relies on two new techniques. The first, called the PDE-ODI principle, converts a broad class of parabolic differential equations into systems of ordinary differential inequalities. This framework bypasses many delicate analytic estimates used in previous work, and yields asymptotic expansions to arbitrarily high order. The second combines a new leading mode condition combined with an "induction over thresholds" argument" to obtain even finer asymptotic estimates (This is joint work with Yi Lai).
]]> http://www-math.umd.edu/research/seminars.html Tue, 24 Mar 2026 12:30:00 EDT Where: MTH 0409
Speaker: Charlie Cifarelli (Stony Brook) -
Abstract: Shrinking gradient Kähler-Ricci solitons (Kähler-Ricci shrinkers) are fundamental objects in the study of the Kähler-Ricci flow, characterizing much of the behavior of finite-time singularities. Recently, Sun--Zhang have developed an algebraic theory for Kähler-Ricci shrinkers, which in particular implies that such spaces are naturally quasiprojective varieties. Moreover, they propose a YTD correspondence between the existence of such a metric and an algebro-geometric notion of K-stability, analogous to and in fact extending the well-known situations for Fano manifolds and Kähler cones. In this talk, I will discuss the proof of one direction of the correspondence, namely that the existence of a Kähler-Ricci shrinker metric implies K-polystability, in the case that the Ricci curvature decays at infinity. This is joint work with Carlos Esparza.
]]> http://www-math.umd.edu/research/seminars.html Tue, 14 Apr 2026 12:30:00 EDT Where: MTH 0409
Speaker: Max Hallgren (Rutgers) -
Abstract: TBA
]]> http://www-math.umd.edu/research/seminars.html Tue, 21 Apr 2026 12:30:00 EDT Where: MTH 0409
Speaker: Mingyang Li (Stony Brook) -
Abstract: It is known from general relativity that axisymmetric stationary black holes can be reduced to axisymmetric harmonic maps into the hyperbolic plane H^2, while in the Riemannian setting, 4d Ricci-flat metrics with torus symmetry can also be locally reduced to such harmonic maps satisfying a tameness condition. We study such harmonic maps and application includes a construction of infinitely many new complete, asymptotically flat, Ricci-flat 4-manifolds with arbitrarily large second Betti number b_2. Joint work with Song Sun.

]]> http://www-math.umd.edu/research/seminars.html Tue, 05 May 2026 12:30:00 EDT Where: MTH 0409
Speaker: Yu-Chi Hou (UMD) -
Abstract: Kähler quantization provides a bridge between infinite-dimensional geometric objects in Kähler geometry and finite-dimensional data arising from spaces of holomorphic sections. In this talk, I will first review this correspondence in the ample case, where it is well understood and plays a central role in the study of canonical metrics. I will then explain how this picture can be extended beyond the ample setting, where smooth positively curved metrics are no longer available. In particular, I will describe how the Monge–Ampère energy can still be recovered from finite-dimensional approximations in the semipositive and big setting. Finally, if time permits, I will outline the idea of the proof.
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