Instructor: David Nadler
Office Hours: by appointment, 815 Evans.
Lectures: Tuesdays and Thursdays 11-12:30pm, 105 Latimer.
Course Control Number: 18349.
Prerequisites: familiarity with Algebraic Geometry (256A-B) and Algebraic Topology (215A-B).
Syllabus:
This course will be an introduction to the algebraic geometry and topology of Lie groups. A primary goal will be to explain the construction of the Langlands dual group via the Geometric Satake correspondence.
- Reductive groups and Lie algebras. Classification of simple groups and Lie algebras. Coincidences.
- sl(2), SL(2), PGL(2). Finite-dimensional representations, Borel-Weil-Bott Theorem. Category O, Beilinson-Bernstein localization. Modular representations.
- Flag varieties. Emphasis on SL(n) and loop group of SL(n). Bruhat/Schubert stratifications. Moment maps. Cohomology and equivariant cohomology.
- Hecke algebras and braid groups. Classical constructions. Hecke categories: constructible sheaves, Soergel bimodules. Beilinson-Ginzburg-Soergel's Koszul duality.
- Geometric Satake correspondences. Perverse sheaves. Tannakian formalism. Derived enhancements.
Lecture notes:
References: