K-theory and quantum fields, spring 2013

Lecturer

Jouko Mickelsson

Scope

10 cu.

Type

Advanced studies

Prerequisites

Basics about groups and representations of Lie algebras, differential geometry; or

the course Mathematical methods in physics III.

Lectures:

On Mondays 10-12 in room C123 and Tuesdays 10 - 12 in room B322. First lecture on Monday, January 21.

Last lectures of the period 3: February 25 and 26.  Period 4: March 18, 19. April 22, 23, 29 and 30. May 6 and 7. 

Exams:

Through seminar presentations/written reports

Bibliography

For the first part of the course, Alan Hatcher: Vector Bundles and K-Theory,http://www.math.cornell.edu/~hatcher/ . More material to be announced during the course.

February 11 - February 25:  Lecture notes luku4.pdf, luku5.pdf. February 26: J. Mickelsson and S. Paycha, "The logarithmic residue density of

a generalised Laplacian", http://xxx.lanl.gov/pdf/1008.3039.pdf  and  Simon Scott, "The residue determinant", Comm. Partial Differential Equations 30 (2005),no. 4-6, 483–507, http://arXiv:math/0406268 . Background reading: Taylor, Michael E. Pseudodifferential operators. Princeton Mathematical Series, 34.Princeton University Press, Princeton, N.J., 1981.

March 18-19: See the Chapter 10 in the book "Heat Kernels and Dirac Operators" by N. Berline, E.Getzler and M. Vergne.  Also p. 90-113 in the

notes by Daniel Freed, "Geometry of Dirac Operators", http://www.ma.utexas.edu/users/dafr/DiracNotes.pdf 

April 22-23:  See the notes  April 22-23.pdf

April 29-30: See  0206139v3.pdf

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