18.S998 for Spring 2016: Introduction to vertex algebras

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


Tomoyuki Arakawa