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====== Research program ====== | ====== Research program ====== | ||

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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: | 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: | ||

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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 | * **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 | * **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 | ||

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