AUTOMNE / FALL 2005
Title: Introduction to Shimura Varieties
Instructor: Peter Clark

Abstract: The course will cover topics in the theory of Shimura varieties, a class of algebraic varieties providing a bridge between Galois theory and automorphic forms. Our focus will be on the examples of modular curves, Shimura curves, and Hilbert and Siegel modular varieties.

We will indicate how properties of modular curves (complex-analytic definition, models over number fields and even over the integers, existence of rational points, special properties and significance of CM points) generalize to the Siegel, Hilbert modular, and quaternionic Shimura varieties. One of the goal of the courses is to prepare graduate students to the topics of the Theme Year, and in particular to the the workshop on Interesction of Arithmetic Cycles and Automorphic Forms which will be held in December.

HIVER / WINTER 2006
Title: Topics in Analytic Number Theory
Instructor: Andrew Granville

Abstract: This course will consist in a series of lectures aimed to prepare graduate students to the topics of the second term of the Theme Year. The subjects presented will be related to classical analysis, analytic number theory, additive number theory and combinatorics.