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Explore advanced mathematical concepts through this comprehensive conference series covering control theory, optimization, and their applications across multiple disciplines. Delve into cutting-edge research presentations from leading mathematicians and researchers at the Centre International de Rencontres Mathématiques, spanning topics from partial differential equations and spectral theory to mean field games and machine learning optimization. Master fundamental techniques including the moment-LP and moment-SOS approaches, POD a-posteriori error estimation for PDE constrained optimization, and spectral inequalities for differential operators. Investigate control problems for particle motion, shape optimization challenges, and stabilization methods for nonlinear PDEs through linear transformations. Discover inverse problem methodologies for linear PDEs using mixed formulations and explore isoperimetry with density applications. Learn about numerical methods for mean field games, including monotone finite difference schemes and variational approaches, while examining capacity expansion games and their applications to power generation investments. Study dynamic formulations of optimal transportation, least squares regression Monte Carlo methods for approximating BSDEs, and pathwise approaches to dynamic robust pricing frameworks. Examine Bayesian inference applications in mathematical imaging through Markov chain Monte Carlo techniques and explore mixture models for complex data analysis. Understand reinforcement learning fundamentals, machine learning applications in signal processing, and the intersection of optimization with quantum computing. Investigate port-Hamiltonian systems, bandwidth bounds based on Herglotz-Nevanlinna functions, and ecological applications in evolutionary cancer control. Explore trajectory inference using Schrödinger bridges, optimal transport theory foundations, and PDE-constrained optimization methodologies. Gain insights into continuous-time reinforcement learning, non-linear market models with default risk, and smooth convex optimization challenges in deep learning contexts.
