Columbia Informal Complex Geometry
and PDE Seminar

Academic Year 2010-2011

Organizers: D.H. Phong, V. Tosatti

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The seminar met on Thursdays from 2.40pm to 4.00pm in 520 Mathematics.

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Schedule

• September 9
  Organizational Meeting

• September 16
  Gábor Székelyhidi - Extremal metrics on blowups - Reference

• September 23
  Jian Song - Kähler-Ricci flow with surgery - Reference

• September 30
  Valentino Tosatti - Kähler-Einstein metrics and stability I - References 1 2

• October 7
  Valentino Tosatti - Kähler-Einstein metrics and stability II - References 1 2

• October 14
  Yuguang Zhang (Capital Normal University Beijing) - Continuity of conifold transitions and flops for Calabi-Yau manifolds - Abstract

  In this talk, we present a proof of a weaker version of the Candelas de la Ossa's conjecture, i.e. conifold transitions and flops for Ricci-flat Calabi-Yau manifolds are continuous in the Gromov-Hausdorff sense.

• October 21
  Special Day on Complex Geometry and PDE - Details

• November 4
  Jacob Sturm - b-stability I - References 1 2

• November 11
  Jacob Sturm - b-stability II - References 1 2

• November 18
  Yu Wang - Viscosity solutions of complex Monge-Ampère equations - References 1 2

• December 2
  Ovidiu Munteanu - Sobolev inequalities on Riemannian manifolds - References 1 2

• December 9
  Nam Q. Le - On boundary regularity of certain Monge-Ampère equations related to Abreu's equation - References 1 2 3

• January 20
  Organizational Meeting

• January 27
  Jian Song - The limiting behavior of the continuity method on toric Fano manifolds - Reference

• February 3
  Valentino Tosatti - Einstein metrics and ε-regularity I - Reference

• February 10
  Valentino Tosatti - Einstein metrics and ε-regularity II - Reference

• February 24
  Yu Wang - Measure estimates on Riemannian metric-measure spaces - Abstract

  In this talk, I shall present an Alexandrov-Bakelman-Pucci type estimate on a Riemannian metric-measure space and deduce Harnack inequalities for the modified Laplacian operator. I would also like to discuss some potential applications of this ABP estimate and Harnack inequalities in the study of complex Monge-Ampère equations.

• March 3
  Gábor Székelyhidi - Extremal metrics on CP² blown up at two points - Reference

• March 10
  Adam Jacob - Existence of approximate Hermitian-Einstein structures on semi-stable bundles - Reference
  
  Jacob Sturm - Analytic test configurations and geodesic rays - Reference

• March 31
  Michael Singer (Edinburgh) - Toric Bergman Asymptotics

• April 7
  Nam Q. Le - Boundary regularity for solutions to linearized Monge-Ampère equations - References 1 2

• April 14
  Valentino Tosatti - Volume estimates for Kähler-Einstein manifolds I - References 1 2

• April 21
  Ovidiu Munteanu - Improved Kato estimates - References 1 2 3
  
  Valentino Tosatti - Volume estimates for Kähler-Einstein manifolds II - References 1 2

• April 28
  Ovidiu Munteanu - Harnack estimates for harmonic functions - References 1 2

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Notes from the talks

• Valentino Tosatti - Lower boundedness of the K-energy on deformations of the Mukai threefold - PDF

• Valentino Tosatti - Kähler-Einstein metrics on Fano surfaces - PDF