D. Heat semigroups and Dirichlet forms on manifolds and metric spaces

Principal Investigators: Sun-Sig Byun (SNU), Panki Kim (SNU), Gerald Trutnau (SNU), Ki-Ahm Lee (SNU)
Scientific Partners: Alexander Grigor'yan (Bielefeld), Michael Hinz (Bielefeld), Michael Röckner (Bielefeld)

One main aim of the project is to develop criteria and techniques to obtain from Dirichlet form theory indeed a "pointwise" analysis, i.e. develop a regularity theory for Dirichlet forms. It is well-known that to get to a pointwise analysis, the study of the heat kernel is fundamental. In the case of singular coefficients there are many open questions in this respect.