Informal Geometric Analysis Seminar (2025.09-2026.06)

ORGANIZED BY: D. Cristofaro-Gardiner, T. Darvas, O. Hershkovits, Y. A. Rubinstein, Y. Liu
DATE: Tuesdays at 3:30 PM.
ROOM: MTH 1313.
PREVIOUS YEARS

The seminar aims to be a relaxed forum for researchers and graduate students interested in geometric analysis, and students of all levels are encouraged to attend and ask questions. Talks will focus on the "big picture" and key ideas and encourage interaction. Talks will be in one of two formats: a) 30-minute talks followed by a ~ 15-30 minute discussion, or b) 50-75 minute talks.

2025 Fall

  • October 21

    • Speaker: Carlos Esparza (Berkeley)

    • Title: Uniqueness of asymptotically conical shrinking gradient Kähler--Ricci solitons

    • 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.

  • November 4

    • Speaker: Ao Sun (Lehigh)

    • Title: Geometry of Mean Curvature Flow near Cylindrical Singularities

    • 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).

  • November 11

    • Speaker: Yueqiao Wu (JHU)

    • Title: K-semistability at infinity

    • 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.

  • November 18

    • Speaker: Benjy Firester (MIT)

    • Title: TBA

    • Abstract: TBA

  • December 9

    • Speaker: Tang-Kai Lee (Columbia)

    • Title: TBA

    • Abstract: TBA

2026 Spring

    Driving and parking directions to UMD: Park in Paint Branch Drive Visitor Lot (highlighted in yellow in the lower right corner of the second map in the previous link), or in Regents Drive Garage (highlighted in the upper right corner). If you arrive after 4pm you do not need to pay: see the instructions in the previous link.