Mathematical Foundations of Quantum Field Theory, 1/16/12 – 1/20/12

Organized by Mike Douglas, Kevin Costello and Arthur Jaffe


Quantum field theory is a rich subject, with a long history in physics and in mathematics. In recent years it has inspired many profound developments in topology, in algebra and representation theory, and in analysis. Given the growing interest in the subject among mathematicians, it seems timely to hold a workshop to review the current state of the field, agree on what has been accomplished and what could be accomplished by a systematic application of the known ideas and techniques, try to identify where new ideas and techniques could have the most impact, and agree on a list of important problems and questions whose resolution would at the least serve as benchmarks to measure our progress, and at best significantly advance the field.



Abdelmalek Abdesselam, Marco Bochicchio, Detlev Buchholz, Johnathan Dimock, Wojciech Dybalski, Dan Freed, Ryan Grady, James Glimm, Steffan Hollands, Yi-Zhi Huang, John Imbrie, Christian Jaekel, David Kaplan, Anton Kapustin, Sheldon Katz, Joachim Krieger, Si Li, Roberto Longo, Sasha Migdal, Werner Nahm, Chiara Nappi, Vincent Rivasseau, Katarzyna Rejzner, Nick Rozenblyum, Yongbin Ruan, Tom Spencer, Peter Teichner, Mithat Unsul, Anastasia Volovich, Robert Wald, Scott Wilson, Edward Witten.

Mathematical Foundations of Quantum Field Theory

SCHEDULE: All talks will be held in SCGP Room 102

Monday 1/16* Tuesday 1/17 Wednesday 1/18 Thursday 1/19 Friday 1/20
9:00am Buchholz: Algebraic quantum field theory. Looking back and looking forward Jaffe: Constructive quantum field theory [video] Kaplan: Lattice supersymmetry and lattice chiral fermions [video] Spencer: Symmetry, Supersymmetry and Duality in Statistical Mechanics
Rozenblyum: Chiral and factorization algebras as an approach to algebraic quantum field theory [video]
11:00am Kapustin: Topological boundary conditions and defects in abelian Chern-Simons theory Yongbin Ruan: Gromov Witten theory of quotient of quintic 3-fold via global mirror symmetry [video] Nahm: The embedding of quantum field theory in mathematics [video] Rivasseau: Matrix and tensor renormalizable models
10:15 am: Teichner: Common structures in field theory and cohomology
11:30 am Henriques: Three-tier CFTs from Frobenius algebras.
2:00pm Hollands: Quantum field theory on curved spacetimes Witten: What One Can Hope To Prove About Three-Dimensional Gauge Theory
Huang: Eigenfunctions on a Riemannian manifold and representations of a vertex operator algebra
Imbrie: Multiscale procedure for diagonalizing Hamiltonians
3:15pm Discussion Discussion 30 min talk: Rejzner: BV Quantization in perturbative algebraic quantum field theory.
Discussion Discussion
4:00pm 30 min talk: Si Li: String field theory on Calabi-Yau manifolds: BCOV and Holomorphic Chern-Simons
4:45pm 30 min talk:
Non-perturbative gauge dynamics on R^3 x S_1
7:00pm Banquet at Danfords Inn and Marina

*Note: Martin Luther King Jr. Day, no videos recorded.

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