Workshop Proposal: Noncongruence modular forms and Galois representations

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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.