Math 285 Number Theory Introduction to the Langlands Program D …

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Math 285. Number Theory. Introduction to the Langlands Program. D. Blasius. This course will introduce the fundamental objects of the theory automorphic …

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Content
Math 285
Number Theory
Introduction to the Langlands Program
D. Blasius
This course will introduce the fundamental objects of the theory automorphic forms (such
as automorphic representations, Hecke algebras, L-functions, L-groups, etc) and show
how the theory works with reference to one of its major goals: the principle of
functoriality. Especially, we will define base change, the transfer between inner forms,
the Converse Theorem, and the Jacquet-Gelbart lift, and apply these to establish the
known cases, in dimension 2, of Artin’s conjecture. We will also explain the attachment
of Galois representations to holomorphic modular forms, putting this result into the larger
framework of Langlands’ global conjectures. If time permits, we will discuss the local
Langlands correspondence and its recent proofs by Harris, Taylor, and Henniart.
The course will explain ideas at the price of sketching many proofs. It is aimed at
students and faculty with some background in Number Theory who want an introduction
to basic topics in the area.
The course meets MW 4:30 to 5:45 in MS 5233, but at the first meeting Monday April 5
we will discuss the possibility of shifting the Monday meeting to Friday….