• Feb. 29, 2024

Biao Ma, A variational inequality approach to Hele-Shaw flow with a moving boundary

Reference: 'A variational inequality approach to Hele-Shaw flow with a moving boundary', Elliott and Janvosky, Proceedings of the Royal Soceity of Edinburgh, 88A, 93-107, 1981

• Jan. 18, 2024

Xin Fu, Strict positivity of Kahler-Einstein currents

Abstract: Given a canonical polarized or Calabi-Yau variety X with klt singularity, we discuss the strict positivity of the canonical Kahler-Einstein current on X based on Guedj-Guenancia-Zeriahi's recent work.

Reference: https://arxiv.org/abs/2305.12422

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• Sept. 14, 2023

Max Hallgren,  A Shrinking Kahler-Ricci Soliton on the Blowup of $CP^1 \times C$, 

Abstract: The classification of Kahler-Ricci solitons with bounded curvature in complex dimension two was completed by Bamler-Cifarelli-Conlon-Deruelle, who constructed a new shrinking soliton as the singularity model of a Toric Kahler-Ricci flow.  This soliton models a finite-time singularity where a (-1)-curve is contracted at the same time as the flow undergoes dimensional collapse. We will overview the main ideas of their proof, including a brief review of some toric geometry, perturbation of J-holomorphic curves, and Bamler's compactness theory.

Reference: https://arxiv.org/abs/2206.10785

• Dec. 15, 2022 

Freid Tong,  Complete Calabi-Yau metrics on complements

Reference: https://arxiv.org/pdf/2203.10656.pdf

• December 20, 2021 （special date, Monday, 10 - 11:30am)

    Bin Guo, Local non-collapsing of Monge-Ampere equations

         Abstract: we will discuss a recent joint with J. Song on the local version of geometric estimates for complex Monge-Ampere equations. We will show how the lower bound of Ricci curvature implies the (local) noncollapsing of metrics.

• December 9

    Biao Ma,  ABP estimate and Sobolev inequalities

         References:

         1. The isoperimetric inequality for a minimal submanifold in Euclidean space, S. Brendle,  Journal of the American Mathematical Society 34.2 (2021): 595-603

          2. Sobolev inequalities in manifolds with nonnegative curvature, S. Brendle,  https://arxiv.org/abs/2009.13717)

• November 11

    Jian Song,  Stability of the J-equation and deformed Yang-Mills equation

• October 28

    Ved Datar,  Non-pluripolar products and Complex Monge Ampere equations with degenerate and singular data, III

• October 21

    Ved Datar,  Non-pluripolar products and Complex Monge Ampere equations with degenerate and singular data, II

• October 7

    Ved Datar,  Non-pluripolar products and Complex Monge Ampere equations with degenerate and singular data, I

      Abstract : I will talk about the work of Boucksom, Berman, Guedj and Zeriahi on a variational approach to solving the Complex Monge Ampere equations in big classes and with a right hand side that is a measure satisfying some properties (for instance, it could be a measure that does not charge pluripolar sets). To make sense of the Monge-Ampere operator, I will first describe the non-pluripolar product introduced by Bedford-Taylor and developed by Boucksom, Eyssidieux, Guedj and Zeriahi. 

• June 10

         Jian Song, Collapsing Calabi-Yau fibrations and uniform diameter bounds, II ( by Yang Li)

• June 3

         Jian Song, Collapsing Calabi-Yau fibrations and uniform diameter bounds ( by Yang Li)

        (https://arxiv.org/pdf/2101.09787.pdf)

• May 27

    Chi Li, Geodesic rays and stability in the cscK problem

    (https://arxiv.org/abs/2001.01366)

• May 13 

    Jacob Sturm, Deligne Pairings and discriminants of algebraic varieties

    (https://arxiv.org/abs/1312.7870) 

• Apr. 29 

    Xin Fu, Log canonical singularities of projective surfaces, II

• Apr. 22 

    Xin Fu, Log canonical singularities of projective surfaces

• Apr. 8

    Bin Guo, Rectifiability of Singular Sets in Noncollapsed Spaces with Ricci Curvature bounded below III

    (https://arxiv.org/abs/1805.07988 by Cheeger, Jiang and Naber)

• Apr. 1

     Bin Guo, Rectifiability of Singular Sets in Noncollapsed Spaces with Ricci Curvature bounded below II

     (https://arxiv.org/abs/1805.07988 by Cheeger, Jiang and Naber)

• Mar. 25

     Bin Guo, Rectifiability of Singular Sets in Noncollapsed Spaces with Ricci Curvature bounded below

     (https://arxiv.org/abs/1805.07988 by Cheeger, Jiang and Naber)

• Mar. 11

     Chi Li, A quantization proof of the uniform Yau-Tian-Donaldson conjecture II

    (https://arxiv.org/abs/2102.02438 by K. Zhang)

• Mar. 4

Ved Datar, Conical Calabi-Yau metrics on affine toric varieties II 

(https://arxiv.org/abs/2005.07053 by Berman)

• Feb. 25

    Chi Li, A quantization proof of the uniform Yau-Tian-Donaldson conjecture I

    (https://arxiv.org/abs/2102.02438 by K. Zhang)

• Feb. 18

Ved Datar, Conical Calabi-Yau metrics on affine toric varieties I

(https://arxiv.org/abs/2005.07053 by Berman)

• Feb. 4

Wanxing Liu, Convergence of cscK metrics on minimal models of general type 

(https://arxiv.org/abs/2012.09934) 

• Jan. 28

Jian Song, Relative volume comparison for the Ricci flow II

(https://arxiv.org/abs/2008.07093 by Bamler)