Moduli spaces and singularities in algebraic and Riemannian geometry – Aug 17 – Nov 20

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Moduli spaces and singularities in algebraic and Riemannian geometry

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Organized by Simon Donaldson (SCGP), Hans-Joachim Hein (Maryland), Henry Guenancia (Stony Brook), Radu Laza (Stony Brook), Yuji Odaka (Kyoto), Song Sun (Stony Brook),Valentino Tosatti (Northwestern)
August 17-November 20th, 2015

Weekly Talks are held in SCGP Rm 313.

The theme of this program is the interaction between algebro-geometric and differential-geometric approaches. In algebraic geometry, one is interested in constructing compact moduli spaces of varieties. Even if one starts with manifolds, the compactification will almost always involve the inclusion of appropriate singular varieties. In a case when the manifolds have canonical metrics, such as Kahler-Einstein metrics, one can approach these questions differential-geometrically, studying the convergence of the metrics and the metric nature of the singular limits. Such ideas are well-established in the case of the moduli of curves and the Deligne-Mumford compactification. The purpose of this program is to make progress in higher dimensions, in the light of a number of recent developments coming from pluripotential theory, Riemannian convergence theory and algebraic geometry. The program will be an opportunity for specialists in the various different fields to interact and share expertise. Topics which will be discussed include:

1. The differential geometric interpretation of the moduli of varieties of general type constructed by Alexeev, Kollar, Shepherd-Barron.

2. Moduli spaces of Fano varieties, and connections with stability.

3. Kahler-Einstein metrics on singular varieties; their singularities and metric tangent cones.

4. Riemannian collapsing and large complex structure limits of Calabi-Yau manifolds.

Program Application is now closed.

Date Time Speaker Title
8/19 2:15 pm Xiaowei Wang GIT stability and  compactification of moduli space
8/21 2:15 pm Jesus Martinez-Garcia On the moduli space of cubic surfaces and their anticanonical divisors
8/26 1:00 pm Helge Ruddat Mini-lectures on the Gross-Siebert program I: Introduction
8/26 2:15 pm Helge Ruddat Mini-lectures on the Gross-Siebert program II: Toric degenerations, affine manifolds
8/27 2:15 pm Jian Song Analytic base point free theorem
8/28 2:15 pm Helge Ruddat Mini-lectures on the Gross-Siebert program III:
Scattering and reconstruction of Calabi-Yau manifolds from degeneration data
9/8 2:15 pm Yuguang Zhang Completion of the moduli space for polarized Calabi-Yau manifolds
9/8 4:00 pm Ben Weinkove Complex surfaces and geometric flows
9/9 1:00 pm Chenyang Xu Introduction of minimal model program and its applications
9/9 2:15 pm Chenyang Xu Introduction of minimal model program and its applications
9/11 2:15 pm Cristiano Spotti CscK resolutions of conically singular varieties:
10/1 2:15 pm Radu Laza KSBA vs. GIT vs. Hodge theory
10/12 2:15 pm Paolo Cascini Toroidal modifications.
10/15 2:15 pm Radu Laza TBA
10/22 2:15 pm Ivan Cheltsov Burkhardt, Todd, Igusa, Beauville and rational quartic threefolds
10/27 2:15 pm Sandor Kovacs Projectivity of the moduli space of stable log-varieties
10/29 2:30 pm Martin de Borbon Asymptotically Conical Ricci-Flat Kahler metrics with cone singularities
11/3 2:30 pm Tomoyuki Hisamoto The strong version of K-stability derived from the coercivity property of the K-energy
11/3 4:00 pm Carl Tipler From the Strominger system to generalized geometry
11/5 2:30 pm Yuji Sano Minkowski problem on Fano polytopes
11/16 12:30 pm Mattias Jonsson A variational approach to the Yau-Tian-Donaldson conjecture. (Part I)
11/16 1:45 pm Mattias Jonsson A variational approach to the Yau-Tian-Donaldson conjecture. (Part II)
11/17 2:30 pm Henri Guenancia Kähler-Einstein metrics on stable varieties