| Date |
Topics |
Sections |
Event |
| Week 1 |
| 03-30 |
Review on Curvature Tensor-Basic Properties |
DC Ch 4.1--4.3 |
|
| 04-01 |
Holonomy and Curvature Tensor--Surface case |
DC Ch 4.4--4.5 |
|
| 04-03 |
Curvature and the Riemannian Holonomy Group I |
NN Lecture 5 |
|
| Week 2 |
| 04-06 |
Curvature and the Riemannian Holonomy Group II |
SA Ch 3.6 |
|
| 04-08 |
Curvature and the Fundamental Groups |
JM Ch 19, DC Ch12 |
|
| 04-10 |
Comparison Theorems-I |
DC Ch 9.1--9.2 |
|
| Week 3 |
| 04-13 |
Comparison Theorems -II |
DC Ch9.3 and Ni-Zheng's Cal PDE paper , Ni's preprint |
|
| 04-15 |
Comparison Theorems -III |
DC Ch 10.1--10.2 |
|
| 04-17 |
Fundamental Groups-I |
DC Ch12.1-12.2 |
|
| Week 4 |
| 04-20 |
Fundamental Groups -II |
DC Ch 12.3 |
|
| 04-22 |
Fundamental Groups -III |
SA Ch 5.1 |
|
| 04-24 |
Volume Non-collapsing and Injectivity Radius |
DC Ch 13.2 and Jour. Diff. Geom. 1982 Paper by Cheeger-Gromov-Taylor |
|
| Week 5 |
| 04-27 |
Riemannian Holonomy Group- I |
NN Lecture 5-6 |
|
| 04-29 |
Riemannian Holonomy Group-II |
NN, Lecture 6, James Simons 1962 Annals of Math. paper |
|
| 05-01 |
Riemannian Holonomy Group- III |
BE, Ch10, James Simons 1962 Annals of Math. paper |
|
| Week 6 |
| 05-04 |
Make-up and Catch-up |
|
|
| 05-06 |
Riemannian Holonomy Group-IV |
NN Lecture 6-7, James Simons 1962 Annals of Math. paper |
|
| 05-08 |
Classification of the Riemannian Holonomy Group |
NN Lecture 7, and James Simons 1962 Annals of Math. paper |
|
| Week 7 |
| 05-11 |
Symmetric Spaces-I |
JM Ch 20 |
|
| 05-13 |
Symmetric Spaces -II |
JM Ch 21 |
|
| 05-15 |
Symmetric Spaces -III |
SA Ch 4.6 |
|
| Week 8 |
| 05-18 |
Symmetric Spaces-I |
SA Ch 4.6 |
|
| 05-20 |
Homogeneous Spaces-I |
SA Appendix 2 |
|
| 05-22 |
Catch-up and Review |
|
|
| Week 9 |
| 05-25 |
Happy Holiday |
|
|
| 05-27 |
Curvature and the Spectrum of the Laplacian Operator |
SA Ch 6.3 |
|
| 05-29 |
Hearing the Volume of a Manifold--Weyl Asymptotics |
SA Ch 6.4, and Leon Simon's Lecture Notes |
|
| Week 10 |
| 06-01 |
Titling Domains and the Spectra |
Polya's Proceedings of LMS paper |
|
| 06-03 |
Kaehler-Einstein Metrics and the Holonomy Group |
BE Ch 11 |
|
| 06-05 |
Kaehler-Einstein Metrics--Estimates |
Ni's CPAM and IJM papers |
|
