Graduate/faculty Seminar
Friday, February 27, 2009, 4:30pm, 119 Physics
Oliver Gjoneski
Eichler-Shimura vs. Harish-Chandra

Abstract:

After a brief introduction of modular forms on the upper half plane and vector-space valued differential forms, we will explore a very classical result (independently due to Eichler and Shimura) which relates certain cohomology groups to cusp forms on the upper half plane of corresponding weight. We will then put our algebraic hat on, and recast this result in modern light, using the theory of Automorphic forms developed by (among others) Harish-Chandra and Langlands. I hope to make the talk accessible to most graduate students. Though the topics we will talk about are related to my research, it is not a research talk, more of an exposition. The first part of the talk should be a breeze for anyone with understanding of some fundamental concepts in Complex analysis and Algebraic Topology (holomorphic functions, differential forms, deRham cohomology.) A course in Representation Theory would be helpful in relating to the concepts in the second part of the talk. [video]

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