Complex Geometry/Singularity Theory

In complex analysis, the research focuses on automorphism groups of Stein manifolds, using geometric tools from Andersén–Lempert theory. There is also research on envelopes of holomorphy and polynomial hulls. This is applied to analytic extension from CR manifolds, supplemented by tools from PDE and Lie theory.

In singularity theory, the research investigates the geometry and topology of singular spaces. This includes the study of invariants and structures that help to understand and classify singular objects, as well as approaches based on degenerations of non-singular spaces and the behaviour of singularities under small perturbations.

For the research topics, we suggest:

• Automorphism groups of Stein manifolds
• Envelopes of holomorphy and polynomial hulls
• CR geometry and analytic extension
• Geometry and topology of singular spaces
• Degenerations and stability of singularities