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Research Group Differential Geometry

Kollegiengebäude Mathematik (20.30)
Room 1.003
Ute Peters

Institut für Algebra und Geometrie
Englerstr. 2
D-76131 Karlsruhe

Office hours:
Mo-Fr 09:00-15:00
Für Studierende:
Mo-Fr 09:15-11:15

Tel.: +49 721 608 43943

Fax.: +49 721 608 46909

AG Differentialgeometrie (Winter Semester 2019/20)

Lecturer: Prof. Dr. Wilderich Tuschmann
Classes: Seminar (0126600)
Weekly hours: 2

Seminar: Thursday 11:30-13:00 SR 2.058
Lecturer Prof. Dr. Wilderich Tuschmann
Office hours: by appointment; during lecture period: Thu. 10:15 - 11:15
Room 1.002 Kollegiengebäude Mathematik (20.30)
Email: tuschmann@kit.edu
Lecturer Dr. Georg Frenck
Office hours: Tuesday, 14:00-15-00
Room 1.036 Kollegiengebäude Mathematik (20.30)
Email: georg.frenck@kit.edu



Lashi Bandara (Universität Potsdam)

Boundary value problems for general first-order elliptic differential operators

The Bär-Ballmann framework is a comprehensive machine useful in studying elliptic boundary value problems (as well as their index theory) for first-order elliptic operators on manifolds with compact and smooth boundary. A fundamental assumption in their work is that an induced operator on the boundary can be chosen self-adjoint. Many operators, including all Dirac type operators, satisfy this requirement. In particular, this includes the Hodge-Dirac operator as well as the Atiyah-Singer Dirac operator. Recently, there has been a desire to study more general first-order elliptic operators, with the quintessential example being the Rarita-Schwinger operator on 3/2-spinors. In general dimensions, every induced boundary operator for the Rarita-Schwinger operator is non self-adjoint.

In this talk, I will present recent work with Bär where we and consider general first-order elliptic operators by dispensing with the self-adjointness requirement for induced boundary operators. The ellipticity of the operator allows us to understand the structure of the induced operator on the boundary, modulo a lower order additive perturbation, as bi-sectorial operator. We use a mixture of methods coming from pseudo-differential operator theory, bounded holomorphic functional calculus, semi-group theory as well as methods arising from the resolution of the Kato square root problem to extend the Bär-Ballman framework.

If time permits, I will also touch on the non-compact boundary case, and potential extensions of this to the L^p setting and Lipschitz boundary.


Vicente Cortes (Universität Hamburg)

Generalized connections and integrability

We characterize the integrability of various structures on Courant algebroids in terms of torsion-free generalized connections. The applications include generalized Kähler and generalized hyper-Kähler structures as particular examples. We do also give a spinorial characterization in the case of regular Courant algebroids. This is based on the theory of Dirac generating operators, for which we develop a new approach based on the geometric data encoding the regular Courant algebroid. This is joint work with Liana David, see arXiv:1905.01977.


Ana Karla Garcia Perez (KIT)



Rafael Dahmen (KIT)



Georg Frenck (KIT)

The action of the mapping class group on spaces of metrics of positive scalar curvature


Philipp Reiser (KIT)



Philipp Reiser (KIT)