August 1-12, 2016
In the thirty years that have passed since they were introduced by Borcherds, vertex algebras have turned out to be extremely useful in many areas of mathematics, such as algebraic geometry, the theory of finite groups, modular functions, topology, integrable system, and combinatorics.
The theory of vertex algebras also serves as the rigorous mathematical foun- dation for two-dimensional conformal field theory and string theory, extensively studied by physicists. The notion of vertex algebras was extended by Beilinson and Drinfeld to chiral algebras, which served as a foundation of the celebrated geometric Langlands program.
We plan to explore yet another perspective of vertex algebras. More precisely, this project follows our previous works [Arakawa-Moreau, Joseph ideals and lisse minimal W-algebras, to appear in J. of Inst. Math. Jussieu] and [Arakawa-Moreau, Sheets and associated varieties of affine vertex algebras, preprint].