I am broadly interested in questions that have a probabilistic or analytic flavor, and take much inspiration from physics as an inexhaustible source of interesting questions and mathematical problems. Such problems often concern models which have the stucture that many simple constituents (particles, spins, graphs, and so on) interact with other spatially close consituents in a simple fashion. The main questions then concern the global collective behavior of all particles.

In particular, one of the main themes in my research has been the understanding of the interaction of many length scales and the emergence of universal behaviour in different contexts, and related to this, the mathematical implementation of the renormalisation group method. Numerous related problems and apparently rather disparate models can be formulated in terms of statistical field theory, interpreted in a broad sense, and the use and exploration of this idea is an important influence in my research.



Proceedings and lecture notes