Number Theory and Representation Theory Conference

数学中有很多传统上独立学科之间相互融合的例子。其中最引人注目的无疑是数论和表征理论之间的深刻互动。在它的现代化身中，这种相互作用导致了椭圆曲线算法的显著进步（例如Shimura-Taniyama猜想，佐藤-泰特猜想，以及Birch和Swinnerton-Dyer猜想对最多为一阶的解析椭圆曲线的证明），并有助于充实一种将算术对象（伽罗瓦表示和动机）与解析对象（自同构形式和表示）联系起来的统一愿景。现在是时候反思数论和表示理论之间的接口，特别是与Gross-Zagier公式有关的最近的发展。这次会议应该有助于将研究生和博士后研究人员介绍到这些重要的数学领域，从而提高数学科学分支的集体专业知识，这对现代信息化经济非常重要。它还应该帮助成熟的研究人员更充分地认识到这一领域不同部分工作之间的联系。会议有望产生一系列有趣的开放问题，这些问题可能会激发未来的研究。

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.