## Math 570 -- Representation Theory and Geometry

- Office: SEO 501

- Office hours: MWF

- Lecture times and place: MWF 10:00-10:50AM, Room 304, Taft Hall

- Prerequisites: Basic algebraic geometry and topology.

- References: These are some of the references that I will be drawing from for the lectures.

- [CG] N. Chriss and V. Ginzburg, Representation theory and complex geometry.

- [J] J.C. Jantzen, Lie Theory, Lie algebras and Representations.

- [H] J.E. Humphreys, Conjugacy Classes in Semisimple Algebraic Groups.

- [OV] A.L. Onishchik, E.B. Vinberg Lie groups Algebraic Groups.

- [HTT] R. Hotta, K. Takeuchi, T Tanisaki, D-Modules, Perverse Sheaves, and Representation Theory.

- [KW] F. Kirwan, J. Woolf, An introduction to Intersection Homology Theory.

### Syllabus:

We will begin with:
- Symplectic geometry (as in [CG] Ch. 1)

- Borel-Moore Homology (as in [CG] Ch. 2)

- Springer theory (as in [CG] Ch. 3 and 4)

After this, the course will get more advanced, with more emphasis on modern
approaches to Springer theory. The topics and references will be chosen as we go along.

Possible keywords are: Perverse sheaves, Intersection cohomology,
Symplectic resolutions, Gromov-Witten theory, Mirror symmetry.
### Lecture notes

Here are the lecture notes. They are mostly copied from [CG] (probably additional mistakes are introduced).