[PAST EVENT] Mathematics Colloquium: Moshe Adrian (University of Toronto)

February 20, 2015
2pm - 3pm
Jones Hall, Room 301
200 Ukrop Way
Williamsburg, VA 23185Map this location
Abstract: The Langlands program is a beautiful convergence of conjectures, ideas, and problems from various areas in mathematics. Originally conceived by Robert Langlands as a way to understand problems from analysis, representation theory, and number theory all at once, the program has expanded into many other directions in recent decades.

I will begin by posing some basic questions in number theory about the prime numbers. After discussing these questions from a historical perspective, I will make a detour and motivate the Langlands program from the point of view of a problem in analysis: that of describing the spectral theory of the Laplacian on certain function spaces. I will then describe a seemingly separate number theoretic problem, which John Tate solved in the 1950's in his Ph.D. thesis.

In the 1960's, Robert Langlands saw that the above spectral theory questions, together with important number theoretic and representation theoretic questions, could be viewed simultaneously in the context of a vast generalization of John Tate's ideas. Langlands' ideas developed into what is now known as the Langlands program.

After discussing how the analytic questions fit into Langlands' larger framework, I will then discuss various number theoretic and representation theoretic questions that immediately arise and that relate to my own research.

Vladimir Bolotnikov