## ENSPM2021 Talk

**Title:** Towards a Euclidean Yang-Mills Theory

**Abstract:** A natural object in the study of Yang-Mills theory is the probability measure on the space of connections whose log-density is given by the Yang-Mills energy. Unfortunately, the infinite-dimensionality of this space, combined with the gauge invariance of the energy functions, cause major difficulties when trying to construct such a measure, especially when the underlying space-time is of dimension greater than 2. In this lecture, we will review some recent progress in this direction in dimension 3.

## Martin Hairer (Imperial College London, UK)

Austrian-British mathematician working in the field of stochastic analysis, in particular stochastic partial differential equations. He is Professor of Mathematics at Imperial College London, having previously held appointments at the University of Warwick and the Courant Institute (NYU). In 2014 he was awarded the Fields Medal. In 2020 he won the 2021 Breakthrough Prize in Mathematics. He worked on variants of Hörmander’s theorem, systematisation of the construction of Lyapunov functions for stochastic systems, development of a general theory of ergodicity for non-Markovian systems, multiscale analysis techniques, theory of homogenisation, theory of path sampling and theory of rough paths and, in 2014, on his theory of regularity structures.