Arithmetic Quantum Field Theory Program Lecture Series

Explore the intersection of arithmetic geometry and quantum field theory through this comprehensive lecture series featuring leading mathematicians discussing cutting-edge research at the boundary of number theory, algebraic geometry, and mathematical physics. Delve into arithmetic topology and its connections to field theory with Minhyong Kim, who examines how topological methods apply to arithmetic problems. Master algebraic quantum field theory fundamentals through Brian Williams' systematic treatment of the mathematical foundations underlying quantum field theoretical structures. Investigate the profound connections between the Langlands program and arithmetic quantum field theory with David Ben-Zvi, exploring how geometric and categorical methods illuminate deep number-theoretic phenomena. Discover factorization algebras and their broad applications with Clark Barwick's generalized framework for understanding algebraic structures in topology and geometry. Learn about period integrals of automorphic forms and residue methods from Omer Offen, connecting classical analytic number theory to modern perspectives. Examine Tate's thesis and p-adic string theory with An Huang, bridging classical algebraic number theory and string-theoretic approaches. Study the integration of braided categories over 3-manifolds with John Francis, exploring topological quantum field theory from a categorical viewpoint. Analyze Shalika periods, functoriality, and arithmetic applications through Dihua Jiang's research on special values of L-functions. Explore relative Langlands duality examples with Chen Wan, investigating geometric and representation-theoretic aspects of the Langlands correspondence. Understand covers of reductive groups and functoriality with Tasho Kaletha's work on extending classical Langlands theory. Follow recent developments in local Arthur packets for classical groups through Baiying Liu's research on representation theory and harmonic analysis. Investigate the Poisson summation conjecture and fiber bundle methods with Jayce Getz's approach to understanding automorphic forms through geometric techniques. Discover the tame categorical local Langlands correspondence with Xinwen Zhu's categorical approach to local Langlands theory. Learn about skein algebras and quantized Coulomb branches from Peng Shan's work connecting knot theory to representation theory and mathematical physics. Conclude with Wei Zhang's presentation on Shtuka special cycles and their generating series, exploring arithmetic intersection theory and its applications to the Langlands program.