Number Theory and Representation Theory Conference

Harvard University, Cambridge MA

Investigators

Abstract

Mathematics abounds with examples of cross-fertilisation between traditionally seperate disciplines. One of the most striking is surely the profound interaction between number theory and representation theory.In its modern incarnation, this interaction has led to notable advances in the arithmetic of elliptic curves (such as the proofs of the Shimura-Taniyama conjecture, the Sato-Tate conjecture, and the Birch and Swinnerton-Dyer conjecture for elliptic curves of analytic rank at most one) and has been instrumental in fleshing out a unifying vision connecting arithmetic objects (Galois representations, and motives) to analytic ones (automorphic forms and representations). The time is appropriate to reflect on the flurry of recent developments at the interface between number theory and representation theory, particularly those related to the Gross-Zagier formula. The conference should help greatly in introducing graduate students and post-doctoral researchers to these important areas of mathematics, thereby enhancing collective expertise in a branch of mathematical science which is of great importance for a modern information-based economy. It should also help established researchers more fully appreciate the connections between work in different parts of this domain. The conference will hopefully produce a list of interesting open problems in the area which may inspire future research.