Number Theory and Representation Theory Conference

数学中有很多传统上相互独立的学科之间相互影响的例子。其中最引人注目的是数论和表示论之间的深刻互动。在它的现代化身中，这种互动导致了椭圆曲线算术的显著进步(如Shimura-Taniyama猜想、Sato-Tate猜想和Birch和Swinnerton-Dyer猜想的证明)，并帮助充实了将算术对象(伽罗瓦表示和动机)与解析对象(自动孤儿形式和表示)联系起来的统一愿景。现在是时候反思数论和表示论之间最近的一系列发展，特别是与格罗斯-扎吉尔公式有关的发展。这次会议应该对向研究生和博士后研究人员介绍这些重要的数学领域有很大帮助，从而提高对现代信息经济非常重要的数学科学分支的集体专门知识。它还应该帮助成熟的研究人员更充分地认识到该领域不同部分工作之间的联系。这次会议有望产生一份该领域有趣的开放问题清单，这可能会启发未来的研究。

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.