RESEARCH INTERESTS

Markov Processes

• singular diffusions (unbounded drifts, reflection problems on rough state spaces, in particular on subsets of infinite dimensional state spaces and moving domains)
• uniqueness problems (pathwise uniqueness, (sub-)martingale problems)
• path regularity (non-explosion, recurrence)
• existence of standard and Hunt processes associated to strongly continuous semigroups on L²-spaces

Symmetric, non-symmetric and generalized Dirichlet forms

• general development

Analysis

• elliptic and parabolic regularity for singular partial differential equations
• analytic and non-analytic strongly continuous semigroups and operator theory