The Department of Mathematics and Statistics at the University of Massachusetts Amherst will host its fifth annual summer school on Physical Mathematics of Quantum Field Theory during the week of July 20-24, 2026. The aim of the workshop is to introduce young researchers on the boundary between mathematics and physics to recent ideas in classical and quantum field theory using notions from complex geometry and algebraic topology. The target audience of the workshop is advanced graduate students and post-docs, from both mathematics and theoretical physics. The schedule will be designed to include a large amount of time for participants to interact. We hope especially to encourage conversations between mathematicians and physicists.
See these links for information about housing and travel.
The speakers this summer are
Zhengping Gui (Shanghai Institute for Mathematics and Interdisciplinary Sciences)
John Huerta (LMU Munich, to be confirmed)
Andrew Neitzke (Yale)
Surya Raghavendran (Yale)
Brian Williams (Boston University)
The lecture series are
The Physics and Mathematics of Class S by Andy Neitzke
These lectures will give an overview of a family of quantum field theories known as "Class S", and some of their applications in physics and mathematics. Topics include: quantum field theories from surfaces; geometry of vacua; connections to other subjects.
Twisted supersymmetry and Calabi-Yau categories by Surya Raghavedran
These lectures will survey methods for extracting holomorphic-topological field theories describing “target space physics” from Calabi-Yau categories, and examples coming from twists of super Yang-Mills and supergravity theories. Topcis include: the Costello-Li conjectures; open topological strings and twisted super Yang-Mills theories; closed topological strings and twisted supergravity.
Chiral algebras and holomorphic quantum field theory jointly by Zhengping Gui and Brian Williams
Topics include: operator product expansions and configuration spaces; chiral algebras; higher Kac--Moody and Virasoro algebras; Feynman diagrams and the residue; examples of chiral algebras and free-field realization; outlook on the future of holomorphic QFT.
TBD by John Huerta