UW Analysis, Geometry and Dynamics Seminar: Bjoern Bringmann

We construct the 2D Yang-Mills-Higgs (YMH) measure via stochastic quantization. To this end, we show global well-posedness and uniform-in-time bounds for the associated Langevin dynamics, which is given by the 2D stochastic YMH equations. A key component of our approach is the further development of techniques in stochastic geometric analysis, combining ideas from geometric analysis and stochastic analysis. These methods yield a manifestly gauge-covariant local existence theory, refined estimates for covariant stochastic objects, and a decay mechanism driven by unstable Yang-Mills connections. This is joint work with S. Cao, M. Hairer, and W. Zhao.