Instructor: Ching-Li Chai

Office: DRL 4N36, Ext. 8-8469.
Office Hours: MW 1:00

General Information

• First meeting: Wednesday 8/30, 1:45 pm, DRL ???.
  
  
• Lectures: MW 1:45--3:14 pm, DRL ???.
  
  
• Topics: Algebras with involutions, classical groups, linear algebraic groups, linear representations of reductive groups, Coxeter groups and (affine) root systems, Hecke algebras, Kazhdan-Lusztig polynomials, Galois cohomology of linear algebraic groups, Hasse principle, approximation in linear algebraic groups, class numbers of linear algebraic groups.
  
  
• Background knowledge: one semester graduate-level algebraic geometry and some algebraic number theory.
  
  
• References:
  • Knus, Merkurjev, Rost and Tignol, The Book of Involutions, AMS, 1998.
  • T. A. Springer, Linear Algebraic Groups, second edition, Birkhauser, 1998
  • N. Bourbaki, Groupes et Algebres de Lie, Chapitres 4, 5, et 6.
  • J. Humphreys, Reflection Groups and Coxeter Groups, CUP, 1990.
  • J. Humphreys, Linear Algebraic Groups, second edition, Springer-Verlag, 1981.
  • A. Borel, Linear Algebraic Groups, second edition, 1991.
  • J.-P. Serre, Galois Cohomology, Springer, 1997.
  • Gartbaldi, Merkurjev, Serre, Cohomological Invariants in Galoi Cohomology, AMS, 2003.
  • V. Platonov and A. Rapinchuk, Algebraic Groups and Number Theory, Academic Press, 1994.

Academic calendar fall 2024

• First day of classes, 8/27
• First meeting, Wednesday 8/28
• Drop period ends, ???
• Grade type change deadline, ???
• Fall break, 10/03--10/06
• Last day to withdraw, 11/08
• Thanksgiving break, ???
• Last day of classes, Monday 12/09