See also: exercises
 Fall semester 2009

 The first weeks you are welcome to
attend the intensive reminder on the basic theory of manifolds.
 Later
announcements will follow

 (01) Week 39, sep 23
 Lecture notes, Lecture 1:
differential operators, scalar and vectorbundle valued.
Principal symbol. Elliptic operators, differential complex, elliptic complex.
Fredholm operators.

 (02) Week 40, sep 30

Lecture Notes, Lecture 2.

 (03) Week 41, oct 7

Lecure Notes, Lecture 3.

 (04) Week 42, oct 14

Schwartz space, Fourier transform, tempered distributions, Sobolev spaces.

See notes Lecture 4 and Notes on Rellich's lemma.

 (05) Week 43, oct 21

Pseudodifferential operator, symbol space, localization,
full symbol, principal symbol.
 See notes Lecture 5.

 (06) Week 44, oct 28
 See notes Lecture 6 and Appendix to Lecture 6
 Kernel of pseudodifferential operator, adjoint, asymptotics for adjoint symbol, pseudolocality.
 Week 45, nov 4
 No lecture.
 (07) Week 46, nov 11
 See notes Lecture 7.

Principal symbol of composition of properly supported pseudodifferential operators,
transformation of pseudodifferential operators under diffeomorphisms,
pseudodifferential operators on a manfifold, restriction and gluing, principal symbol on
a manifold, composition and adjoint.

 (08) Week 47, nov 18

See Notes for Lecture 8.

Pseudodifferential operators on vector bundles, construction of parametrices, regularity
theorem for elliptic operators.

 (09) Week 48, nov 25
 One hour lecture, see Notes for Lecture 9.

Definition of local Sobolev space by using elliptic pseudodifferential operator;
invariance of local Sobolev space; local Sobolev space with values in bundle,
continuity of pseudodifferential operator. Fredholm property of elliptic
pseudodifferential operator on compact manifold. Index independent of Sobolev order.
 Two times 45 minutes: Exercises done in front of class.

 (10) Week 49, dec 2
 See Notes for Lectures 10  11.
Section 10.1: connections, Section 10.2: curvature,
Section 10.3: characteristic classes
(by applying invariant polynomials on local curvature matrices and glueing),
Start of 10.4. 
 (11) Week 50, dec 9
 See Lecture 10 from 10.4 in Notes for Lectures 1011.

 (13) Week 51, dec 16
 See Lecture 11 in Notes for Lectures 1011.

Last update: 21/62009