Quantum Field Theory and Topological Phases via Homotopy Theory and Operator Algebras
June 30, 2025 @ 9:00 am - July 11, 2025 @ 5:00 pm
Workshop on Quantum Field Theory and Topological Phases via Homotopy Theory and Operator Algebras
Dates: June 30 – July 11, 2025
Location: CMSA, 20 Garden Street, Cambridge MA and Max Planck Institute for Mathematics, Bonn, Germany
This event is a twinned workshop at the CMSA (Harvard) and the Max Planck Institute for Mathematics (Bonn). Lectures will alternate between the two sites, watched simultaneously on both sides, and there will be opportunities for dialogue between the locations. The first week will contain four pedagogical lecture series; lecturers and locations are
Michael Hopkins, Harvard (CMSA)
Alexei Kitaev, Caltech (CMSA)
Pieter Naaijkens, Cardiff (MPIM)
Bruno Nachtergaele, UC Davis (MPIM)
The second week will consist of research talks.
Participants are strongly encouraged to attend at the location that minimizes travel and hence the ecological impact of the conference.
Online application for the Harvard CMSA location. The application deadline was March 16, 2025.
To apply for the MPIM-Bonn location, please visit https://www.mpim-bonn.mpg.de/qft25
Quantum Field Theory (QFT) and Quantum Statistical Mechanics are central to high energy physics and condensed matter physics; they also raise deep questions in mathematics. The application of operator algebras to these areas of physics is well-known. Recent developments indicate that to understand some aspects QFT properly a further ingredient is needed: homotopy theory and infinity-categories. One such development is the recognition that symmetry in a QFT is better described by a homotopy type rather than a group (so-called generalized symmetries). Another one is the work of Lurie and others on extended Topological Field Theory (TFT) and the Baez-Dolan cobordism hypothesis. Finally, there is a conjecture of Kitaev that invertible phases of matter are classified by homotopy groups of an Omega-spectrum. This workshop will bring together researchers and students approaching this physics using different mathematical techniques: operator algebras, homotopy theory, higher category theory, etc. The goal is to catalyze new interactions between different communities. At the workshop recent developments will be reviewed and hopefully progress can be made on two outstanding problems: the Kitaev conjecture as well as the long-standing goal of finding a proper mathematical formulation for QFT.
Organizers:
- Dan Freed, Harvard University CMSA & Math
- Dennis Gaitsgory, MPIM Bonn
- Owen Gwilliam, UMass Amherst
- Anton Kapustin, Caltech
- Catherine Meusburger, University of Erlangen-Nürnberg