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

Twinned workshop on "Quantum Field Theory and Topological Phases via Homotopy Theory and Operator Algebras", June 30 - July 11, 2025 [5]

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 ofoperator 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) [6] 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 [7], Harvard Mathematics (CMSA)
A. Kitaev [8], Caltech (CMSA)
P. Naaijkens [9], Cardiff University (MPIM)
B. Nachtergaele [10], 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.

Application:

The application deadline was March 16, 2025.

For the application for online participation please click here. [11]
The application for in-person participation at MPIM Bonn/Germany is closed.
The application for in-person participation at CMSA, Harvard/USA is closed.

To apply for the CMSA-Harvard location, please visit cmsa.fas.harvard.edu/event/mpqft25/ [12] .

Contact:

qft25$@$mpim-bonn$.$mpg$.$de [13]

Warning: Hotel scam alert: There is a hotel scam going around contacting people from conferences regarding accommodation. Please DO NOT reply to them or give out any credit card/personal information! We do not work with any travel agencies and we will only contact you through official MPIM e-mail-addresses. Read more here. [14]

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Policy for the Max Planck Society against discrimination, harassment and violence. [15]