Algebra and Geometry lecture series.

This lecture series was given in Fall 2021 and the topic was Quantizations in positive characteristic and applications. Click here for an abstract including a list of prerequisites and references.

Videos are available here.

  • Lecture 0: Prerequisite lecture about basics of quantizations. Includes the definition and examples of Poisson algebras, the definition and examples of filtered quantizations, the definition of formal quantizations and their relation with filtered ones. Finally, there is a discussion of quantizations of schemes.
  • Sept 8, 4-5pm: Office hour on Lecture 0.
  • Sept 9, Lecture 1: Quantizations via Hamiltonian reduction, Notes.
  • Sept 16, Lecture 2: Quantization commutes with reduction, Notes. Differential operators in characteristic p, Notes.
  • Sept 22, office hours, 3-4pm.
  • Sept 23, Lecture 3: Frobenius constant quantizations. Derived equivalences from quantizations. Notes.
  • Sept 30, Lecture 4: Splitting bundles. Notes.
  • Oct 7, Lecture 5: The case of Springer resolution and connection to modular representations of semisimple Lie algebras. Notes (updated 10/8).
  • Oct 14, Lecture 6: The case of Springer resolution and connection to modular representations of semisimple Lie algebras, cont'd, Notes.
  • Oct 21: no lecture.
  • Oct 28: Lecture 7: Hilbert schemes and Procesi bundles. Hamiltonian reduction. Notes.
  • Nov 4, Lecture 8: Quantizations of symmetric powers and Hilbert schemes. Notes.
  • Nov 11, Lecture 9: Construction of Procesi bundles via quantizations in characteristic p. Notes.
  • Nov 18, Lecture 10: Construction of Procesi bundles, cont'd. Lifting to characteristic 0 and rational Cherednik algebras. Notes.
  • Nov 25, no lecture.
  • Dec 2, Lecture 11: Macdonald positivity, Notes.
  • THE END of this lecture series.