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A. Analysis of differential and integro-differential equations
Nonlinear dispersive equations, singular integrals, nonlocal generators of jump processes
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B. Dynamics of interacting systems
Dynamical systems on configuration spaces, fractional Fokker-Planck equations, nonlocal evolution equations, stochastic Kuramoto model, synchronization, metastability
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C. Random matrices and Mathematical Physics
Universal limit laws for real and complex eigenvalues, asymptotic analysis using free probability and orthogonal polynomials
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D. Heat semigroups and Dirichlet forms on manifolds and metric spaces
Stochastic differential equations and Sobolev regularity on infinite-dimensional and fractal state spaces, singular drifts, propagation speed on manifolds and metric spaces, heat kernel estimates for operators with singular coefficients and magnetic energy forms