## **Algebra and Geometry lecture series.**

**Time: Th 4-6, location: zoom **
(password was sent by Ivan on Aug 30).

Organized by Ivan Losev.

This seminar features lecture series by participants who are usually Yale faculty and postdocs.

Videos are posted in Yale box.
In case they cannot access the Yale box, participants outside of Yale
should contact Ivan.

The first lecture series is by Ivan and the topic is *Quantizations in positive characteristic and applications*.
Click here for an abstract including a list of prerequisites and references.

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. Quantizations.*