Program
Moduli, Hypergeometric Functions and Automorphic Forms
Student No.:50
Time:Mon/Thu. 10.10-12:00, 2015-09-07 ~ 2015-09-28
Instructor:Jerome William Hoffman  [Louisiana State University]
Place:Conference Room 3, Floor 2, Jin Chun Yuan West Building
Starting Date:2015-9-7
Ending Date:2015-9-28
 

Description:

We will study families of algebraic varieties which are hypergeometric in the sense that their periods satisfy Picard-Fuchs differential equations of generalized hypergeometric type. Typically these families are parametrized by quotients of bounded symmetric domains and are solutions to moduli problems. We are interested in the motives defined by these varieties, and will discuss their zeta and L-functions. In addition to discussing general theory, the emphasis will be on a series of examples, starting with Legendre’s family of elliptic curves. Higher-dimensional examples include families of K3-surfaces and Calabi-Yau varieties.  Also, we will present the theory of hypergeometric motives recently introduced by H. Cohen and F. Rodriguez-Villegas.

 

 

Prerequisite:

Graduate level Algebra, Complex Analysis and Topology. Some familiarity with Algebraic Geometry, Number Theory, Elliptic Curves, Modular Forms is helpful but not required.

 

 

Reference:

Henri Cohen, $L$-functions of hypergeometric motives, slides of a talk, available at http://www.math.ubordeaux1.fr/$\sim$hecohen/ow.pdf

 

Deligne, P.; Mostow, G. D. Monodromy of hypergeometric functions and nonlattice integral monodromy. Inst. Hautes {\'E}tudes Sci. Publ. Math. No. 63 (1986), 5--89.

 
Yoshida, Masaaki, Hypergeometric functions, my love. Modular interpretations of configuration spaces. Aspects of Mathematics, E32. Friedr. Vieweg & Sohn, Braunschweig,