Seminar Talk
Colloquium
Speaker: Yiannis Sakellaridis, Johns Hopkins University
Title: Zeta functions and symplectic duality
When: Thursday, October 10, 4:10 PM - 5:00 PM
Where: C304 Wells Hall
Contact: Francois Greer (greerfra@msu.edu)
The Riemann zeta function was introduced by Euler, but carries Riemann's name because he was the one who extended it to a meromorphic function on the entire complex plane, and discovered its importance for the distribution of primes. It admits a vast class of generalizations, called L-functions, but, as in Riemann's case, one usually cannot prove anything about them without relying on seemingly unrelated integral representations.
In joint work with David Ben-Zvi and Akshay Venkatesh, we elucidate the origin of such integral representations, showing that they are manifestations of a duality between nice Hamiltonian spaces for a pair (G,ˇG) of "Langlands dual" groups. Over the geometric cousins of number fields -- algebraic curves and Riemann surfaces -- such dualities had been anticipated and constructed in many cases by Gaiotto and others, motivated by mathematical physics.
In this talk, I will give an introduction to this array of ideas, assuming only some basic definitions in Galois theory and topology.