Differential operators on manifolds: where analysis meets geometry

23.01.2019, 14:00  –  Haus 9, Raum 2.22
Institutskolloquium

Jan Slovák (Brno, Czech Republic), Nadine Große (Freiburg)

14:00 Nadine Große (Freiburg): Boundary value problems: an approach via bounded geometries
In this talk, we consider boundary value problems on domains with non smooth boundaries. For the Dirichlet problem on domains with smooth boundary we have good elliptic regularity results  at hand. If the boundary is no longer smooth, this is in general no longer the case. In the talk we approach this problem by transferring it to non-compact manifolds with a nice geometry -- the bounded geometry. This gives a more general framework how to handle Dirichlet (or Dirichlet-Neumann mixed) boundary value problems for domains with a larger class of singularities on the boundary. This is joint work with Bernd Ammann (Regensburg) and Victor Nistor (Metz).

15:00 Tea and Coffee break

15:30 Jan Slovák (Brno, Czech Republic): Calculus on Symplectic Manifolds
We shall discuss analogues on symplectic manifolds of de Rham complex on differential manifolds. Such constructions lead to Fedosov structures. We shall relate these complexes to the algebraic construction of the Bernstein-Gelfand-Gelfand complexes on partial flag manifolds. This is based on joint work with Michael Eastwood (ANU).

17:30 musical evening in Café Lehmann with singing performance by Jan Slovák