Probabilistic methods in quantum field theory

Trimester Program

May 5 - August 15, 2025

Organizers: Roland Bauerschmidt, Eveliina Peltola, Ellen Powell, Rémi Rhodes, Eero Saksman

Quantum field theories (QFTs) have been successfully applied, throughout the lat 70 years, to model and analyze diverse physical phenomena; in particular, critical behavior in statistical mechanics, and interactions of fundamental particles. However, a rigorous mathematical framework to construct and understand these theories is still limited. This program will further pursue this direction, building on recent developments towards QFT coming from random geometry and probability theory. In particular, the goal is to bring together researchers with different viewpoints and expertise on this multifaceted topic.

With this comined expertise, the program aims at addressing some of the main challenges and key open questions in the field, including in the following areas: 

• advances in quantum gauge theories in 3D and 4D
• rigorous constructions of exactly solvable quantum field theories, especially in 2D
• more generally, analysis of probabilistic aspects of quantum field theories
• the theory of phase transitions, in particular for systems with continuous symmetry, and related phenomena

The program will include an introductory summer school and three workshops. For further information concerning these events, please see the above-mentioned links to the corresponding websites.