Workshop Proposal: Noncongruence modular forms and Galois representations

由Winnie Li和Ramin taklo - bighash组织的“非同余模形式和伽罗瓦表示”研讨会将于2011年4月29日至5月1日在芝加哥伊利诺伊大学举行。重点将放在非同余模形式、p进Hodge理论、伽罗瓦表示和高维约化群上的自同构形式之间的相互作用和联系。将有六位来自美国机构的受邀演讲者：Matthew Emerton（西北大学）、Toby Gee（哈佛大学和西北大学）、Kiran Kedlaya（麻省理工学院和加州大学圣地亚哥分校）、wenching Winnie Li（宾夕法尼亚州立大学）、Tong Liu（普渡大学）和Ling Long（爱荷华州立大学）。29日和30日将举行特邀演讲人的讲座，5月1日将举行博士和研究生的讲座。这是UIC一年一度的奥利弗·阿特金纪念讲座和研讨会的一部分。模形式及其相关的伽罗瓦表示在现代数论中具有普遍的重要性。例如，这些物品在安德鲁·怀尔斯？费马的证明？s大定理。模形式有两种基本形式：一种与同余群有关，另一种与非同余群有关；同余模形式理论的理解要好得多。这个工作坊集中在更神秘和更少理解的非同余模形式。尽管所有的模形式，无论是否同余，都希望编码深度算术信息，但在非同余模形式的情况下，这些信息不容易访问。然而，伽罗瓦表示的算术理论的最新进展，使得以以前不可能的方式理解非同余模形式成为可能。

A workshop "Noncongruence modular forms and Galois representations", organized by Winnie Li and Ramin Takloo-Bighash, will take place April 29-May 1, 2011 at the University of Illinois at Chicago. The focus will be on the interplay and connections between non-congruence modular forms, p-adic Hodge theory, Galois representations, and automorphic forms on higher dimensional reductive groups. There will be six invited speakers all from American institutions: Matthew Emerton (Northwestern), Toby Gee (Harvard and Northwestern), Kiran Kedlaya (MIT and UC San Diego), Wen-ching Winnie Li (Penn State), Tong Liu (Purdue), and Ling Long (Iowa State University). The lectures by invited speakers will happen on April 29 and 30, and May 1 is reserved for talks by participating recent PhDs and graduate students. This is part of the annual Oliver Atkin Memorial Lecture and Workshop at UIC. Modular forms and their associated Galois representations are of ubiquitous importance in modern Number theory. These objects, for example, played a prominent role in Andrew Wiles? proof of Fermat?s Last Theorem. Modular forms come in two basic flavors: the ones associated with a congruence group, and those associated with noncongruence groups; the theory of congruence modular forms is far better understood. This workshop concentrates on the more mysterious and less understood noncongruence modular forms. Even though all modular forms, congruence or not, are expected to encode deep arithmetic information, this information is not easily accessible in the case of noncongruence modular forms. Recent progress in the arithmetic theory of Galois representations, however, has made it possible to understand noncongruence modular forms in ways that was previously impossible.