Elliptic Operators and Index Theory (Masters Course)
Contact Information
Contact: Chris Bourne cbourne [at] nagoya-u.jp, bourne.christopher.jack.x7 [at] f.mail.nagoya-u.ac.jp
Office Hours: Tuesday 12:00–13:00, Thursday 14:00–15:00, or by appointment.
Location: Room 419, Humanities Common Facility Building (A4② on the Campus Map)
Extra time (not always guaranteed): Friday afternoon in Room 203 of the Mathematics Building.
Contents (tentative)
- Fredholm operators
- Singular integral operators on the circle
- Differential operators on Euclidean space
- Differential operators on Riemannian manifolds
- Vector bundles and connections
- Clifford algebras and Dirac operators
- Index theory and applications in geometry and physics
Somewhat final lecture notes: Link
References
Students are encouraged to look at several references and find a text that suits them. Some options are given below.
D. Bleecker, B. Booss-Bavnbek: Index Theory with Applications to Mathematics and Physics, International Press, 2013.
J. Roe: Elliptic operators, topology and asymptotic methods, Second edition, Chapmann & Hall/CRC, 1998.
H. Lawson, M. Michelsohn: Spin Geometry, Princeton University Press, 1989.
P. Gilkey: Invariance Theory, the Heat Equation and the Atiyah-Singer Index Theorem, Second edition, CRC Press, 1995
N. Berline, E Getzler, M. Vergne: Heat Kernels and Dirac Operators, Springer, 1992.
T. Friedrich: Dirac Operators in Riemannanian Geometry, American Mathematical Society, 2000.
古田幹雄: 整数定理，岩波書店，2018.
Additional materials and resources will be distributed where necessary.
日本人学生へのメッセージ
この科目は英語での数学を使う機会があって，挑戦してみてほしいです．