Categoria:
Seminari di Algebra e Geometria
Data e ora inizio evento:
Data e ora fine evento:
Aula:
Sala di Consiglio
Sede:
Dipartimento di Matematica, Sapienza Università di Roma
Speaker:
Charles Young (University of Hertfordshire)
Vertex algebras formalise the properties of what physicists would call operator product expansions (OPEs) in chiral conformal field theories (CFTs). One way to motivate the axioms of vertex algebras is by first defining conformal blocks in genus zero, and then studying their limits in which marked points collide. One would like to generalise this story to higher settings: "higher" in the sense of higher dimensions, but also in the sense of higher/homotopy/differential graded (dg) algebras. In recent months, an elegant and comparatively accessible instance of such higher vertex algebras has been introduced by Garner and Williams. They are called raviolo vertex algebras, and are associated to manifolds of real dimension three admitting a transverse holomorphic foliation; that is, roughly, manifolds having one complex-holomorphic and one topological direction. I will describe these raviolo vertex algebras, and go on to show that they, too, arise from the limiting behaviour of certain raviolo conformal blocks, which I will introduce in the talk. In particular I will describe a certain configuration space of ravioli, and a model in dg commutative algebras of the derived sections of its structure sheaf. This talk is based on work in preparation, joint with Luigi Alfonsi and Hyungrok Kim.

