Tuesdays and Thursdays, 1:00-2:30, Room 2-151.
Course description:
An introduction to vertex algebras and their representations theory.
Boson fermion correspondence, affine vertex algebras, Virasoro algebra, W-algebras, and algebras of chiral differential operators. Connection to classical representation theory. Conformal blocks and fusion rules. Details of representation theory of W-algebras and applications.
Feb. 2. A small application of vertex algerbas
Feb. 4. Basic of vertex algebras I
Feb. 9. Basic of vertex algebras II
Feb. 11. Basic of vertex algebras III
Feb. 16. Jet schemes and vertex algebras
Feb. 18. Associated varieties of vertex algebras
Feb. 23. Vertex algebras modules and Zhu's algebras
Feb. 25. Chiral differential operators on G
Mar. 2. Moore-Tachikawa conjecture
Mar. 4. BRST reduction
Mar. 9. Chiral Hamiltonian reduction I
Mar. 11. Chiral Hamiltonian reduction II
Mar. 18. Tachikawa conjecture
Mar. 29. Slodowy slices and W-algebras
Mar. 31 Equavariant W-algebras
Apr. 5. No lecture
Apr. 7. No lecture
Apr. 12. Proof of Kac-Wakimoto vanishing theorem via equavariant W-algebras
Apr. 14. More vanishing theorem and BRST reduction of associated varieties
Apr. 19. No Lecture
Apr. 21. No Lecture
Apr. 26. W-algebras at the critial level
Apr. 28. Kac-Wakimoto admissible representations I
May 3. Kac-Wakimoto admissible representations II
May 5. Associated varieties of Kac-Wakimoto admissible representations
May10. Minimal models of principal W-algebras
May 12. Minimal models of principal W-algebras II, Open problems