The aim of this International Research Training Group is to advance Mathematics in a joint initiative between Bielefeld University and Seoul National University. The focus will be on the mathematical analysis of problems which exhibit singular features or the in uence of randomness. Our research program is structured into the following four research areas:

• A. Analysis of differential and integro-differential equations
  Nonlinear dispersive equations, singular integrals, nonlocal generators of jump processes
• B. Dynamics of interacting systems
  Dynamical systems on configuration spaces, fractional Fokker-Planck equations, nonlocal evolution equations, stochastic Kuramoto model, synchronization, metastability
• C. Random matrices and Mathematical Physics
  Universal limit laws for real and complex eigenvalues, asymptotic analysis using free probability and orthogonal polynomials
• 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