Geometry and Number Theory Seminar
Thursday, April 7, 2016, 1:05pm, 130 Physics
Wushi Goldring (Washington U in St. Louis)
Algebraicity of automorphic representations

Abstract:

One striking implication of Langlands' conjectures for number fields is that many automorphic representations which are initially defined by analytic and/or representation-theoretic means should have deep algebro-geometric properties, ranging from the algebraicity of Hecke eigenvalues, to the existence of associated Galois representations and ultimately pure motives. An example of a long-standing open problem in this area which admits an elementary formulation is to prove that Maass forms of eigenvalue 1/4 have algebraic Hecke eigenvalues. Two approaches have been used to verify Langlands' predictions: (1) Finding and exploiting a direct link with algebraic geometry and (2) Using Langlands' Functoriality Principle. I will discuss the possibilities and limitations of the two approaches and report on recent work on each approach. The results using the geometric approach are joint work with Jean-Stefan Koskivirta, see arXiv:1507.05032.

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