Conformal blocks from VOAs: an algebro-geometric perspective (SS 24, Chiara Damiolini)
Abstract: In this three-day course I will present and summarize joint works with A. Gibney, N. Tarasca and D. Krashen on the properties of (and open questions concerning) spaces of conformal blocks associated with representations of Vertex Operator Algebras (VOAs). I will start by explaining how these spaces, defined first by Ben-Zvi and Frenkel for smooth curves, can be extended to nodal curves. The consequence will be that spaces of conformal blocks define sheaves on moduli of stable pointed curves which are further equipped with a projectively flat logarithmic connection. A central result we have established is that these sheaves are "closed under tautological maps" (e.g., they satisfy the factorization theorem), and when the VOA they depend on is rational they define vector bundles. Moreover, we will see how, under appropriate conditions imposed on the VOA, the sheaves of conformal blocks define a cohomological field theory. No familiarity with VOAs is required.
Coordinates:
Lectures will be in held in person and streamed:
- Tuesday, 25th June 14:15 to 15:45. Room 433, Geomatikum
- Tuesday, 2nd July 14:15 to 15:45. Room 433, Geomatikum
- Tuesday, 9th July 14:15 to 15:45. Room 433, Geomatikum