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Twinned workshop on "Quantum Field Theory and Topological Phases via Homotopy Theory and Operator Algebras"

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Organiser(s): 
Daniel Freed (Harvard University), Dennis Gaitsgory (MPIM Bonn), Owen Gwilliam (University of Massachusetts, Amherst), Catherine Meusburger (FAU Erlangen-Nürnberg), Anton Kapustin (Caltech)
Date: 
Mon, 30/06/2025 - 09:00 - Fri, 11/07/2025 - 15:00
Location: 
MPIM Lecture Hall

Twinned workshop on "Quantum Field Theory and Topological Phases via Homotopy Theory and Operator Algebras", June 30 - July 11, 2025

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.

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:

M. Hopkins (CMSA)
A. Kitaev (CMSA)
P. Naaijkens (MPIM)
B. Nachtergaele (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.

Application:

Please consider carefully where / how the participation makes the most sense for you and fill the relevant form. The application deadline is March 16, 2025.

For the application for in-person participation at MPIM Bonn/Germany please click here.
For the application for in-person participation at CMSA, Harvard/USA please click here.
The application for only virtual participation will follow soon.

Contact:

qft25$@$mpim-bonn$.$mpg$.$de

 

 

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