In the Thouless-Anderson-Palmer approach to mean-field spin glasses, the free energy is presented as the infimum of a functional which TAP defined over the space of all possible magnetization vectors, subject to a convergence condition. Its self-averaging over exponentially many solutions at low temperature seems to be taken for granted, though…

Although lattice Yang-Mills theory is easy to rigorously define, the construction of a satisfactory continuum theory is a major open problem in dimension d ≥ 3. Such a theory should assign a Wilson loop expectation to each suitable collection L of loops in d-dimensional space. One classical approach is to try to represent this expectation as a…

The Adler-Bardeen non-renormalization is a basic property of anomalies with important physical implications, ranging from particle physics to condensed matter. We prove its validity in lattice models at a non-perturbative level, focusing in particular on fermion-vector boson models in 3+1 and 1+1 dimensions. The proof relies on regularity…

I will give an account of the recent progress in probability and in number theory to understand the large values of the zeta function on the critical line, especially in short intervals. The problems have interesting connections to statistical mechanics of disordered systems, both in their interpretations…

In this talk we explain recent results relating the six-vertex model and the Kardar-Parisi-Zhang (KPZ) universality class. In particular, we describe how the six-vertex model can be used to analyze stochastic interacting particle systems, such as asymmetric exclusion processes, and how infinite-volume pure…