Probability Seminar
Building 2, 182 MEMORIAL DR, Cambridge, MA
Speaker: Sky Cao (UPenn) Title: Construction of the 2D Yang-Mills-Higgs measure Abstract: I discuss the construction of the 2D Yang-Mills-Higgs (YMH) measure via stochastic quantization, or i.e. by Markov Chain Monte Carlo. To do so, we show global well-posedness and uniform-in-time bounds for the associated Langevin dynamics, 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. Based on joint work with B. Bringmann, M. Hairer, and W. Zhao.