L-functions, functoriality, and quantization

Seminar: 
Colloquium
Event time: 
Wednesday, December 15, 2021 - 4:15pm
Speaker: 
Yiannis Sakellaridis
Speaker affiliation: 
Johns Hopkins
Event description: 

Abstract:

L-functions of number fields, elliptic curves, and other objects of diophantine geometry, are ubiquitous in number theory, but their study almost always relies on the Langlands correspondence, which predicts that they encode “eigenfrequencies” of arithmetic manifolds, and realizes them as “period integrals” of automorphic forms on such manifolds (e.g., of modular forms).

After introducing these notions, I will explain how the idea of quantization of symplectic manifolds can provide a symmetric interpretation of the duality between L-functions and periods (based on ongoing joint work with D. Ben-Zvi and A. Venkatesh), and will present evidence for its relevance to the Langlands functoriality conjecture (“different arithmetic drums share the same eigenfrequencies”), based on recent work of mine on the rank-1 case.