CMI Workshop:
Automorphic Forms in Moduli Problems of Schottky and Brill-Noether Type
March 28 – 30, 2008
The study of moduli spaces is one of the most relevant and active areas in algebraic geometry and complex analysis; its interaction with mathematical physics is one of the most vibrant and fast-moving fields of mathematics at the outset of the twenty-first century. This area is also rooted in classical, nineteenth-century mathematics, where some of the deepest theories and still outstanding questions originated. The aspect we wish to address is the dual nature of certain special functions, in their dependence on moduli as automorphic forms, and their dependence on a Fourier-Mukai dual variable, which describes a moduli space of bundles-theta functions being the prime example.
Schedule
Friday, March 28
| 10:15-10:45 | Registration |
| 11:00-12:00 | Hershel Farkas, Generalizations of Thomae's Formula to the Case of Z_n Curves |
| 12:00-1:30 | Lunch |
| 1:30-2:30 | Alan Mayer, Some Problems in Abelian Functions |
| 3:00-4:00 | Samuel Grushevsky, Local Structure of the Singularities of the Theta Divisor |
| 4:30-5:30 | Yaacov Kopeliovich, Theta Constants Identities for Jacobians of Cyclic 3-Sheeted Covers of the Sphere and Representations of the Symmetric Group |
Saturday, March 29
| 11:00-12:00 | Discussion: Higher Weierstrass Points on the Klein Curve; Gauss' AgM; Prym Varieties as Spectral Manifolds; the Higher-Rank Heat Equation |
| 12:00-2:00 | Lunch |
| 2:00-3:00 | Joe Harris, Title (TBA) |
| 4:00-5:00 | Brainstorming Session on Open Questions |
| 6:00 | Dinner |
Sunday, March 30
| 12:30-1:30 | Igor Krichever, Algebraic-geometrically integrable equations and the Riemann-Schottky problem |
| 2:00-3:00 | Leon Takhtajan, Calculus on Algebraic Curves |
| 4:00-5:00 | Jay Jorgenson, Theta functions, Arakelov invariants, and hyperbolic heat kernels |
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