CMI Workshop:
K3's: Modular Forms, Moduli, and String Theory

March 20 – 23, 2008

In the past year, there has been a new interaction between the Gromov-Witten theory (or topological string theory) of K3 surfaces and Heegner divisors (or Noether-Lefschetz loci) on the moduli space of K3 surfaces. As a consquence, new results and many new conjectures have appeared in the form of identities involving modular forms, hypergeometric series, and K3 moduli on the one hand and the geometry of these classical Noether-Lefschetz loci on the other. Our goal in the workshop is to bring mathematicians from the various areas involved in the subject together. A narrower goal is to make progress on this circle of rather concrete conjectures.

Schedule

Thursday, March 20

9:00-9:30 Registration
9:30-10:30 Rahul Pandharipande, Questions about the K3 surface
11:00-12:00 Albrecht Klemm, The Solution of the Topological B-model
2:30-3:30 Eduard Looijenga, Noether-Lefschetz loci in the K3 Moduli Space and Automorphic Forms
4:00-5:00 Greg Moore, Wall crossing formula for BPS states and some applications

Friday, March 21

9:30-10:30 Davesh Maulik, Gromov-Witten Theory of k3 Surfaces
11:00-12:00 Albrecht Klemm, Topological String and Almost Holomorphic Automorphic Forms
2:30-3:30 Wei Zhang, Modular Generating Functions of Special Cycles
4:00-5:00 Emanuel Scheidegger, Topological Strings on K3 Fibrations

Saturday, March 22

9:30-10:30 Jim Bryan, The Quantum McKay Correspondence
11:00-12:00 Conan Leung, Yau-Zaslow Formula
2:30-3:30 Alina Marian, Theta Dualities on Moduli of Sheaves on K3 Surfaces
4:00-5:00 Kai Behrend, Attempts at Categorifying Donaldson-Thomas Theory

Sunday, March 23

9:30-10:30 Brendan Hassett (joint with Yuri Tschinkel), Flops and Ample Cones of Holomorphic Symplectic Fourfolds
11:00-12:00 Yuri Tschinkel (joint with Bogomolov and M. Korotiaev), A Torelli Theorem for Curves over Finite Fields

Organizers

Participants