Research
- 2010-10-29 Revised version of the paper on determinants with Boris Vertman
Regular-singular Sturm-Liouville operators and their zeta-determinants- Oberseminar Globale Analysis
Better late than never:
Here is the paper with Pflaum and Moscovici Connes-Chern character for manifolds with boundary and eta cochains, based on svn rev 246.
Recent activities
Conference on Noncommutative Geometric Methods in Global Analysis, organized with Alain Connes, Alexander Gorokhovsky, Markus Pflaum, Bahram Rangipour
Conference on Spectral Analysis on Noncompact Manifolds
Organized by Clara Aldana, Daniel Grieser, Eugenie Hunsicker, Matthias Lesch, Alexander Strohmaier
2011
- Analyse Geometrique, CIRM, Luminy, 17.01.-21.01.2011
- Non-commutative geometry, scattering theory and the Witten index, ESI, Wien, 31.01.- 04.02.2011
- The Ninth Annual NCGOA Spring Institute, Vanderbilt University, Topics: Index theory and Hopf algebras, 09.05. - 18.05.2011
- Noncommutative Geometry,
MFO Oberwolfach, 11.09.-17.09.2011
2012
- K-Theory and Quantum Fields (M. Ando, A. Carey, H. Grosse, J. Mickelsson), ESI, Wien, 21.05.-27.07.2011
Topics in Global Analysis II - Local Index Theory
Master Programme V4B4
This course is a continuation of my lecture course which I started last semester. Besides completing the proof of the Local Index Theorem for Dirac type operators on closed manifolds I plan to cover (some of) the following topics
- Boundary value problems and the Atiyah-Patodi-Singer Index Theorem
- Conical singularities (Cheeger, Bruening-Seeley, ML)
- Elements of the b--calculus of Melrose
- Noncommutative Residue, Dixmier trace and the local index theorem in noncommutative geometry
Literature
- Berline, Getzler, Vergne: Heat kernels and Dirac operators, Springer 1992
- Gilkey: Invariance theory, the heat equation, and the Atiyah-Singer index theorem, Second edition, 1995
- Lawson, Michelsohn: Spin geometry, Princeton Univ. Press, 1989
- Roe, J. Elliptic operator, topology, and asymptotic methods, Second edition, Longman, Harlow, 1998.
- M. Shubin: Pseudodifferential operators and spectral theory. Springer, 1978
- B. Booss, K. P. Wojciechowski: Elliptic boundary problems for Dirac Operators. Birkhäuser, 1993