A confluence of ideas from geometry, algebra, and analysis is involved in this project. Vilonen plans to work on the following questions on perverse sheaves and D-modules, with applications to representation theory: 1) micro-local Riemann- Hilbert correspondence, 2) applications of perverse sheaves to representation theory of finite-dimensional algebras, Harish- Chandra modules, and character sheaves. In addition, some other directions are suggested, foremost a geometric approach to the Langlands program.
