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Explore the mathematical foundations of stochastic quantisation applied to Yang-Mills-Higgs theory in three dimensions through this 59-minute conference talk presented at BIMSA's ICBS2025. Delve into the rigorous mathematical framework that connects stochastic processes with quantum field theory, focusing specifically on the Yang-Mills-Higgs model in 3D spacetime. Learn about the technical challenges and innovative approaches used to establish well-posedness of the stochastic partial differential equations arising in this context, including regularity theory, renormalization techniques, and convergence results. Gain insights into how stochastic quantisation provides an alternative pathway to understanding quantum field theories through probabilistic methods, with particular emphasis on gauge theories coupled to scalar fields. Discover the latest developments in constructive quantum field theory and the mathematical tools required to handle the non-linear interactions and gauge invariance properties inherent in Yang-Mills-Higgs systems.
