Presentation of the collaboration

Quantum Field Theory (QFT) underpins both high-energy and condensed matter physics with overwhelming experimental success. It has profoundly influenced nearly all areas of mathematics, including analysis, geometry, topology, and algebra. The most significant contemporary challenges in QFT are of a non-perturbative nature, and this offers a compelling challenge for mathematicians.

In recent decades, substantial advances in stochastic analysis and random geometry have introduced powerful probabilistic tools for rigorously addressing non-perturbative aspects of QFT. Conformally invariant processes like the Schramm–Loewner evolution allow analysis of the fractal structure of field theories, the theory of Regularity Structures offers insights into field singularities, and Multiplicative Chaos provides a mathematical foundation for Liouville Quantum Gravity. Frameworks such as the Mating-of-Trees exemplify how these tools can be fruitfully combined, yielding deep rigorous results in statistical physics

This collaboration brings together experts in probability, analysis, and mathematical physics to develop a unified probabilistic foundation for Euclidean QFT, with the goal of enabling non-perturbative analysis of central models and advancing the interface between QFT and mathematics.