Math 517-1, D-modules in birational geometry

Instructor: Mihnea Popa

Mihnea Popa
Office: Lunt 226
Tel: 847-491-5576
  • Meeting times: MWF 10-10:50, Lunt 101
  • Office hours: M 3-4pm and by appointment
  • References: For the first part of the course I will be mainly using "A primer of algebraic D-modules" by S. C. Coutinho, "D-modules, perverse sheaves, and represenatation theory" by R. Hotta, K. Takeuchi and T. Tanisaki, and "Algebraic D-modules" by A. Borel et al.
  • Other useful references: I will introduce new references as we go. For instance, later on we will make use of M. Saito's "Modules de Hodge polarisables", and C. Sabbah and C. Schnell's "MHM project"
Brief course description: We will start with a general introduction to D-modules in algebra and geometry (various operations, holonomicity, V-filtration, Bernstein-Sato polynomial, resolutions, etc.). This will be followed by a study of their connections with Hodge theory, especially the study of the Hodge filtration on D-modules of Hodge theoretic origin. We will then study the connection between Hodge-theoretic D-modules and birational geometry (most likely next quarter). Notes will be posted occasionally.