Title: On Some Topics in Automorphic Representations
Authors: Dihua Jiang, University of Minnesota
Abstract: Automorphic forms or more classically modular forms have been a very active subject in mathematics in the past two centuries. The classical theta functions in the theory of representing a number by a sum of squares and in the theory of Riemann zeta functions are typical examples. Modular forms related to elliptic functions and elliptic curves are more sophisticated examples. More recently, modular forms have been used to interpret discoveries in mathematical physics (string theory, Mduality, for instance), algebraic geometry (the theory of motives, for instance) and number theory (representations of Galois groups, for instance). The conjectural framework for the theory of automorphic forms and its intrinsic relations to algebraic geometry and number theory is called the Langlands Program. The relations of automorphic forms to mathematics physics is roughly referred as the geometric Langlands program.
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