Contents

• A. C* actions on projective varieties

• B. The B-B decomposition

• C. The Homology Basis Theorem

• D. A generalization of the Homology Basis Theorem

• E. Holomorphic vector fields and the cohomology ring

• F. Borel's Theorem and holomorphic vector fields

• G. Holomorphic vector fields with one zero

• H. A remark on rationality

• I. Closing remarks

Contents

• A. Duality in the character ring of a finite Coxeter group

• B. Truncation and Duality in the character ring of a finite group of Lie type

• C. Main theorems on duality

• D. Applications to Springer's Theorem and a conjecture of MacDonald

• E. Some additional results

Contents

• A. Lattices in Lie groups

• B. Finite generation and finite presentation

• C. Normal subgroups

• D. Normal subgroups (continued)

Contents

• A. Elementary theory

• B. Induced modules

• C. Infinitesimal methods

• D. Rational cohomology

• E. Lusztig's conjecture

Contents

• A. Motivation

• B. Evident restrictions

• C. Isotropic semi-simple groups over fields

• D. Short remarks on O'Meara's method

• E. Tits' results on homomorphisms of Lie groups

• F. Rigidity, strong rigidity, and superrigidity of lattices

• G. Quotient groups of lattices

• H. Lattices in PSO(n,1) and PSU(n,1)

• I. Concluding remarks