Math 262: Geometry of the Complex Monge-Ampère Equation

Monday, Wednesday, Friday, 12-1pm, Science Center 507

Course website:


Tristan Collins
Email: tcollins at math dot harvard dot edu
Office: Science Center 233

Course References


This is approximate. I will attempt to keep track of all the references used in class.

Date Material Problems/Handouts
Jan. 26-30 Kahler Manifolds: References: (GH)-Chapter 0, (Sz)-Chapter 1

Feb. 2-6 Yau's Theorem The C2 and C3 estimates for the Complex Monge-Ampère equation: (PSS), (Sz)- Chapter 3. The Pogorelov estimate for the real Monge-Ampère equation: (Gut)- Chapter 4.
Feb. 9-13 Yau's Theorem The C0 estimate. The Moser iteration (PSS). The exponential Moser iteration (W).
Feb. 16-20 Yau's Theorem, Limits of CY manifolds The ABP estimate (Bl), (PSS). Uniform Diameter Bound (To).
Feb. 23-27 Limits of CY manifolds The Diameter Bound (To).
Mar. 2-6 Limits of CY manifolds Gromov-Hausdorff Convergence, Gromov's compactness theorem (Ro),(CCT)
Mar. 9-13 Pluripotential Theory Currents, PSH functions (D), (Ko), (GH)
Mar. 23-27 Pluripotential Theory The Bedford-Taylor theory of the Monge-Ampere operator (BT), (D), (GZ) and the C0 estimate of Kolodziej (PSS), (Ko), (EGZ)
Mar. 30 - Apr. 3 Pluripotential Theory and the Non-collapsing case Existence of Kahler currents in nef classes (DP) and the non-Kahler locus (CoT)
Apr. 6-10 The Non-Collapsing Case Uniform estimates, identification of the GH limit (To), (CoT), (RZ), (RZ2)
April 13-15 The Collapsing Case Uniform Estimates (To2)