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Research


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

2012


Topics in Global Analysis II - Local Index Theory

Master Programme V4B4

Prof. Dr. Matthias Lesch,

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
Prerequisites Contents of part I of this course, Linear Algebra I-II, Analysis I-III and basic knowledge of differential topology. Familiarity with the material covered in my Bachelor course Globale Analysis I,II, e.g. tensor calculus, differential forms, pseudodifferential operators, unbounded operators in Hilbert space.

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

Time and Venue

Tuesday 10(c.t.)-12, Thursday 8(c.t.)- 10 LWK 0.006, Mathematikzentrum