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Mathematics Colloquium

Tuesday, October 17, 2023
4:00pm to 5:00pm
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Linde Hall 310
The orbit method, microlocal analysis and applications to L-functions
Paul Nelson, Department of Mathematics, Aarhus University,

L-functions are generalizations of the Riemann zeta function. Their analytic properties control the asymptotic behavior of prime numbers in various refined senses. Conjecturally, every L-function is a "standard L-function" arising from an automorphic form. A problem of recurring interest, with widespread applications, has been to establish nontrivial bounds for L-functions. I will survey some recent results addressing this problem. The proofs involve the analysis of integrals of automorphic forms, approached through the lens of representation theory. I will emphasize the role played by the orbit method, developed in a quantitative form along the lines of microlocal analysis.

For more information, please contact Math Department by phone at 626-395-4335 or by email at [email protected].