| Speaker: Jethro van Ekeren Affiliation: Universidade Federal Fluminense, Rio de Janeiro Time: 3pm Thursday, 24 January, 2019 Location: 303e.257 |
| (Joint work with Reimundo Heluani.) The minimal models form one of the simplest classes of conformal field theory (vertex algebra in mathematical language), and are very important in statistical mechanics. With each vertex algebra one may canonically associate two affine schemes: its 'singular support' and its 'associated scheme'. Let us call a vertex algebra 'classically free' if its singular support coincides with the arc space of its associated scheme. We show that the minimal models of type (2, 2k+1), the so called 'boundary minimal models', are classically free and all others are not. The coordinate rings of the two schemes in question are naturally graded and the isomorphism yields an equality of graded dimensions which recovers the celebrated Rogers-Ramanujan identity. Towards the end of the talk I will discuss the context in which the question of classical freeness arose for us: the geometric Langlands program, and more specifically the computation of chiral homology of families of elliptic curves with degenerate fibre. |