Constructing factorization spaces and chiral algebras from the Hilbert scheme of points.
Event details
| Date | 14.04.2015 |
| Hour | 15:15 › 17:00 |
| Speaker | Emily Cliff, Oxford |
| Location | |
| Category | Conferences - Seminars |
Given a complex surface X, Nakajima and Grojnowski have shown that the cohomology H of Hilb(X) is naturally a representation of the Heisenberg Lie algebra modelled on the cohomology of X, and is isomorphic as a representation to the Fock space. It follows that H acquires a canonical structure of vertex algebra, and hence that we can associate to H a factorization or chiral algebra over any curve C. Motivated by this result, we attempt to construct this factorization algebra directly using the Hilbert scheme of X. In the first half of this talk, we will review some of the ideas of Grojnowski and Nakajima, and introduce the notions of factorization spaces and factorization algebras; then we show how we can use Hilb(X) to produce examples of each over curves and surfaces. In the second half, we will introduce the category of chiral algebras, which is Koszul dual to the category of factorization algebras. Then we will study the factorization algebra living over the surface X in more detail: we will compute its chiral homology and some other properties.
Practical information
- Informed public
- Free