Workshop Proposal: Noncongruence modular forms and Galois representations

由温妮李和拉明塔卢-比格阿什组织的“非全等模形式和伽罗瓦表示”研讨会将于2011年4月29日至5月1日在芝加哥的伊利诺伊大学举行。 重点将放在非全等模形式，p-adic霍奇理论，伽罗瓦表示和自守形式之间的相互作用和连接更高的维约化群。将有六位来自美国院校的特邀演讲者：Matthew Emerton（西北大学）、Toby Gee（哈佛和西北大学）、Kiran Kedlaya（麻省理工学院和加州大学圣地亚哥分校）、Wen-ching温妮Li（宾夕法尼亚州立大学）、Tong Liu（普渡大学）和Ling Long（爱荷华州州立大学）。受邀演讲者的讲座将于4月29日和30日举行，5月1日将由最近参与的博士和研究生进行演讲。这是UIC年度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·怀尔斯的作品中扮演了重要角色。费马的证明最后定理。模形式有两种基本类型：与同余群相关的模形式和与非同余群相关的模形式;同余模形式的理论更容易理解。这个研讨会集中在更神秘和更少了解的非全等模形式。尽管所有的模形式，全等或不全等，都被期望编码深层算术信息，但在非全等模形式的情况下，这些信息不容易获得。 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全等模形式成为可能。

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.