16.10.17 – Statistical Mechanics and Conformal Field Theory: an Ising Model Perspective.

“For his work on the mathematical and probabilistic aspects of statistical mechanics and in particular for his resolution of several landmark problems regarding the Ising model at the critical temperature.”

A major success of modern physics lies in the unification of two disciplines: Quantum Field Theory, which studies high energy physics and elementary particles, and Statistical Mechanics, which describes large-scale phenomena arising from individual behaviors. While fascinating, this unification presently lacks a mathematically rigorous understanding.

The Ising model lies at the heart of Statistical Mechanics. It consists of atomic entities which tend to interact with their neighbors; those display remarkable large-scale behaviors. This model has found many applications, from magnetism to ecology, going through to image processing.

In the 1980s, Quantum Field Theory led to spectacular predictions for the Ising model. The recent mathematical proofs of these predictions is one of the key contributions of Prof. Hongler. Microscopic symmetries are connected with macroscopic ones, also giving insight into the geometry of random curves arising in the model, and into its deep algebraic structures.

This new technology, which links small and large scales, has the potential to deepen the mathematical understanding of both Quantum Field Theory and Statistical Mechanics. Furthermore it brings new ideas to tackle exciting conjectures for Ising-type models. Thanks to the universality of such models, these results also brings new insights into other fields as well.