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Explore the mathematical framework of symmetries in singular stochastic partial differential equations through this advanced mathematical lecture delivered at the International Conference on Branching Systems 2025. Delve into the theoretical foundations and applications of symmetry principles when dealing with SPDEs that exhibit singular behavior, examining how these symmetries can be identified, classified, and utilized in mathematical analysis. Learn about the intersection of stochastic analysis, partial differential equations, and symmetry theory, with particular focus on how symmetry considerations can provide insights into the structure and solutions of singular SPDEs. Gain understanding of current research developments in this specialized area of mathematical physics and stochastic analysis, including theoretical frameworks and potential applications in modeling complex systems with inherent randomness and singular characteristics.
