Learning seminar on complex geometry

We meet regularly on Thursday from 10am - ∞. 

Zoom Meeting Link

Meeting ID: 950 9901 5487

Password: 800344


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

 


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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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




Freid Tong,  Complete Calabi-Yau metrics on complements


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




    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.




    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)




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



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



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



    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. 



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

    


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

    

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


 

    Chi Li, Geodesic rays and stability in the cscK problem


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



    Jacob Sturm, Deligne Pairings and discriminants of algebraic varieties

  

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



    Xin Fu, Log canonical singularities of projective surfaces, II



    Xin Fu, Log canonical singularities of projective surfaces


    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)


     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)

     

     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)

     

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

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


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

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


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

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


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

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


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

(https://arxiv.org/abs/2012.09934) 


Jian Song, Relative volume comparison for the Ricci flow II

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