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.
A.O.L (Oliver) Atkin, a noted mathematician of international fame and professor emeritus at the University of Illinois at Chicago, died on December 23, 2008 at the age of 83. He made lasting contributions to the theory of numbers: the theory of modular forms (Atkin-Lehner operators, congruences, modular forms for non-congruences groups), theory of partitions, and cryptography (Schoof-Elkies-Atkin Algorithm), among others. He was also a pioneer of the use of computers in mathematics. He was born in England and worked at Bletchley Park in World War II. He completed his doctorate at Cambridge in 1952 under John Littlewood. He joined the faculty at the University of Illinois at Chicago in 1972. Atkin remained mathematically active until his death. The annual Atkin Memorial Lecture is aimed at remembering Oliver Atkin's lasting contributions to mathematics and the University of Illinois. The previous speakers are Ken Ono (2009) and Steve Kudla (2010). In 2011 Winnie Wen-ch'ing Li of Penn State gave the Atkin Lecture on Friday April 29, 2011 at 3 PM. The lecture was followed by a two day workshop, funded by the NSF, with the title of Noncongruence modular forms and Galois representations on April 30 and May 1. The focus was on the interplay and connections between noncongruence modular forms, p-adic Hodge theory, Galois representations, and automorphic forms on higher dimensional reductive groups. The first day (and the first talk on the second day) was devoted to talks by the invited speakers: Matthew Emerton (Northwestern), Toby Gee (Northwestern) Jerome W. Hoffman (LSU), Kiran Kedlaya (MIT and UCSD), Winnie Wen-ch'ing Li (Penn State; Principal Speaker), Ling Long (Iowa State), and Tong Liu (Purdue) . These lectures covered the necessary background for a modularity theorem for certain Galois representations coming from non-congruence modular forms, and as such provided the main intellectual contribution of the workshop. The second day was reserved for lectures by seven younger participants in the early stages of their careers (graduate students and postdocs). These lectures provided a much needed exposure for these young mathematicians. In order the publicize the works of these young mathematicians, the slides of their lectures are posted on the website of the workshop: www.math.uic.edu/~rtakloo/atkin2011.html As announced on the website of the workshop, the lectures were videotaped and are available free of charge to those who are interested. To summarize: * Intellectual merits of the workshop: Covering recent advances in modularity of certain Galois representations coming from non-congruence modular forms. * Broader impact: Lectures by younger participants, workshop website containing slides of lectures, video recordings of lectures available free of charge.