CMSA

CMSA Quantum Field Theory Program
2027-08-30 09:00 - 2028-05-05 17:00 (America/New_York) | Hybrid – G10
CMSA Quantum Field Theory Program
Dates: August 30, 2027 – May 5, 2028
Location: Harvard CMSA, 20 Garden Street, Cambridge MA
Quantum field theory (QFT) has long been a subject with a large influence on mathematics, yet there is still no unified mathematical framework that encompasses all viewpoints. Constructive QFT and Algebraic QFT—typified by the Wightman and Haag-Kastler axiom systems, respectively—have many achievements in relativistic and Euclidean QFT, but they do not include Wick-rotated theories on compact manifolds and so miss many of the geometric, topological, and algebraic developments of the past several decades. These developments include supersymmetric QFT and applications to geometry and topology, generalized symmetries in QFT, and a robust mathematical theory of topological QFTs. The more recent Segal and Costello-Gwilliam axiom systems do accommodate some of these developments, but they are largely disjoint from the analytic progress. Techniques from probability theory and stochastic PDE have been used to advance traditional constructive and algebraic QFT; they have also been applied to obtain rigorous results in two-dimensional conformal field theory and Euclidean lattice gauge theories. There has also been recent progress in quantum lattice systems, revealing surprising new bridges between operator algebras and topology.
This special year at CMSA aims to shape the direction of the field by bringing the analytic and geometric threads of mathematical QFT into closer contact. The program will gather a diverse group of mathematicians together with physicists who enjoy close interactions with mathematicians. The year will be organized around the four focus areas listed below. There will be several short courses and one weeklong workshop for each of these focus areas. All lectures will be hybrid.
FOCUS AREAS
First Semester

Axiomatic approaches to QFT
Symmetry, anomalies, and topology

Second Semester

Probabilistic methods in QFT
Supersymmetry, geometry, and moduli spaces

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We welcome long-term visitors as well as short-term visitors and online participants. If you would like to participate in the program, other than the workshops, please click here: Visitor Form
If you would like to be on a mailing list for information and announcements about this special year, please click here: Subscribe to the CMSA QFT Program Mailing List

Organizers:

Sourav Chatterjee (Stanford University)
Clay Cordova (University of Chicago)
Dan Freed (Harvard University)
Anton Kapustin (Caltech)
Constantin Teleman (University of California, Berkeley)
