Columbia Informal Complex Geometry
and PDE Seminar
Academic Year 20102011
Organizers: D.H. Phong, V. Tosatti
The seminar met on Thursdays from 2.40pm to 4.00pm in 520 Mathematics.
Schedule

September 9
Organizational Meeting

September 16
Gábor Székelyhidi  Extremal metrics on blowups
 Reference

September 23
Jian Song  KählerRicci flow with surgery  Reference

September 30
Valentino Tosatti  KählerEinstein metrics and stability I 
References 1 2

October 7
Valentino Tosatti  KählerEinstein metrics and stability II 
References 1 2

October 14
Yuguang Zhang (Capital Normal University Beijing)  Continuity of conifold transitions and flops for CalabiYau 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 Ricciflat CalabiYau manifolds are continuous in the GromovHausdorff sense.

October 21
Special Day on Complex Geometry and PDE
 Details

November 4
Jacob Sturm  bstability I 
References 1 2

November 11
Jacob Sturm  bstability II 
References 1 2

November 18
Yu Wang  Viscosity solutions of complex MongeAmpère 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 MongeAmpère 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 εregularity I
 Reference

February 10
Valentino Tosatti  Einstein metrics and εregularity II
 Reference

February 24
Yu Wang  Measure estimates on Riemannian metricmeasure spaces
 Abstract
In this talk, I shall present an AlexandrovBakelmanPucci type estimate on a Riemannian metricmeasure 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 MongeAmpère equations.

March 3
Gábor Székelyhidi  Extremal metrics on CP^{2} blown up at two points  Reference

March 10
Adam Jacob  Existence of approximate HermitianEinstein structures on semistable 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 MongeAmpère equations  References 1 2

April 14
Valentino Tosatti  Volume estimates for KählerEinstein manifolds I  References 1 2

April 21
Ovidiu Munteanu  Improved Kato estimates 
References 1
2
3
Valentino Tosatti  Volume estimates for KählerEinstein manifolds II  References 1 2

April 28
Ovidiu Munteanu  Harnack estimates for harmonic functions 
References 1
2
Notes from the talks

Valentino Tosatti  Lower boundedness of the Kenergy on deformations of the Mukai threefold  PDF

Valentino Tosatti  KählerEinstein metrics on Fano surfaces  PDF