Rice University Department of Mathematics Colloquium

Periods, L-functions and abelian varieties

4:00 pm Thursday, October 15, 2015
Keerthi Madapusi Pera (U. Chicago)

Abstract: Periods are a special class of complex numbers, admitting a deceptively simple definition, which lie somewhere in between the worlds of algebraic and transcendental numbers. L-functions are analytic objects that generalize the Riemann zeta function and have similarly deep and mysterious arithmetic properties.

In this talk, I'll review the definitions and basic properties of both these types of objects and explain some deep and highly conjectural relationships between periods and the Taylor coefficients of L-functions.

In particular, I'll explain a special case of such a relationship for periods of certain abelian varieties, originally conjectured by P. Colmez, which has led to a proof by J. Tsimerman of the Andre-Oort conjecture for Siegel modular varieties.

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