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26:645:744 Advanced topics in geometry (Fall 2016)
Course schedule
For general important dates in the semester, see the academic calendar here.
This course schedule is subject to change, refer to last version online (and make sure you refresh the page).
Class time and location:
Monday: 1pm-2:20pm, Smith Hall 204
Wednesday: 11:30am-12:50pm, Smith Hall 204
Office hours:
Monday: 10:30am-11:30am, Smith Hall 308
Wednesday: 10:30am-11:30am, Smith Hall 308
Contact: brice@loustau.eu
| Date | Topic | Special |
|---|---|---|
| Wed 09/07 | Welcome, Introduction, Chap. 1: History | First day of class |
| Mon 09/12 |
Chap. 2: Riemannian geometry. 2.1: Manifolds and tensor fields |
|
| Wed 09/14 | 2.1: Manifolds and tensor fields | |
| Mon 09/19 | 2.2: Riemannian metrics | |
| Wed 09/21 | 2.3: Connections | |
| Mon 09/26 | 2.4: Curvature | |
| Wed 09/28 | 2.5: Symmetric spaces | |
| Mon 10/03 | 2.6: Jacobi fields | |
| Wed 10/05 | 2.7: Constant curvature metrics | |
| Mon 10/10 |
Chap. 3: Models of hyperbolic space 3.1: Hyperboloid model |
|
| Wed 10/12 | 3.1: Hyperboloid model | |
| Mon 10/17 | 3.2: Poincaré ball model | |
| Wed 10/19 | 3.2: Poincaré ball model | |
| Mon 10/24 | - | Class cancelled |
| Wed 10/26 | 3.2: Poincaré ball model 3.3: Klein model | |
| Mon 10/31 | 3.3: Klein model | |
| Wed 11/02 | 3.3: Klein model | |
| Wed 11/09 | 3.3: Klein model | |
| Mon 11/14 | 3.4: Relation between models | |
| Wed 11/16 | 3.5: Other models | |
| Mon 11/21 |
Chap. 4: Hyperbolicity in metric spaces, boundary at infinity and classification of isometries 4.1: Gromov hyperbolicity and CAT(k) spaces |
|
| Wed 11/23 | - | Class cancelled (Wed 11/23 follows a Friday schedule) |
| 11/24-11/27: Thanksgiving recess | ||
| Mon 11/28 | 4.2: Gromov boundary, visual boundary and horospheres | |
| Wed 11/30 | 4.3: Classification of isometries | |
| Mon 12/05 | 4.4: Ideal boundary of hyperbolic space 4.5: Classification of isometries of hyperbolic space |
|
| Wed 12/07 |
Chap. 5: $\mathbb{H}^2$, $\mathbb{H}^3$ and $\mathbb{C}P^1$ Chap 5.1: The complex projective line, the Riemann sphere and Möbius transformations Chap 5.2: $\mathbb{H}^2$ |
|
| Mon 12/12 | Chap 5.3: $\mathbb{H}^3$ Chap. 6: Classical hyperbolic geometry Chap 6.1: 2-dimensional hyperbolic geometry |
|
| Wed 12/14 |
Chap 6.1: 3 and n-dimensional hyperbolic geometry Concluding remarks on the course |
Regular classes end |