(Newton Institute, 2009)

**Lectures by P. Achar on derived categories and perverse sheaves:**

- Lecture I (derived categories and derived functors)
- Lecture II (t-structures, perverse sheaves)
- Lecture III (D-modules, representation theory)
- Lecture IV (Decomposition theorem, purity)
- Lecture V (pointwise purity, Springer correspondence, coherent sheaves)

**Lectures by Ram on symmetry, polynomials and quantization:**

- Lecture I (DAHA)
- Lecture II (Chevalley groups, alcove walks)
- Lecture III (Cherednik algebras)
- Lecture IV (symmetric functions)

**Lectures by J. Chuang on sl_2-categorification and derived equivalences:**

- Lecture I (Broue's conjecture)
- Lecture II (sl_2-categorification)
- Lecture III (perverse equivalences)

**Lectures by Rouquier on higher representations of Lie algebras:**

- Lecture I (2-representation theory)
- Lecture II (generators and relations)
- Lecture III (2-representations)
- Lecture IV (simple representations)
- Lecture V (braid relations)

**Lectures by Vogan on representations of real reductive groups:**

- Lecture I (unitary representations, real groups, geometry of the flag variety)
- Lecture II (real forms, Cartan bijection)
- Lecture III (D-modules)
- Lecture IV (Beilinson-Bernstein, Harish-Chandra modules, signatures)

*Last updated: 13 December, 2009*