Seminar series
Date
Mon, 24 Jan 2011
Time
15:45 -
16:45
Location
L3
Speaker
Andre Henriques
Organisation
Universiteit Utrecht
Roughly speaking, a quantum field theory is a gadget that assigns algebraic data to manifolds. The kind of algebraic data depends on the dimension of the manifold.
Conformal nets are an example of this kind of structure. Given a conformal net, one can assigns a von Neumann algebra to any 1-dimensional manifold, and (at least conjecturally) a Hilbert space to any 2-dimensional Riemann surfaces.
I will start by explaining what conformal nets are. I will then give some examples of conformal net: the ones associated to loop groups of compact Lie groups. Finally, I will present a new proof of a celebrated result of Kawahigashi, Longo, and
Mueger:
The representation category of a conformal net (subject to appropriate finiteness conditions) is a modular tensor category.
Conformal nets are an example of this kind of structure. Given a conformal net, one can assigns a von Neumann algebra to any 1-dimensional manifold, and (at least conjecturally) a Hilbert space to any 2-dimensional Riemann surfaces.
I will start by explaining what conformal nets are. I will then give some examples of conformal net: the ones associated to loop groups of compact Lie groups. Finally, I will present a new proof of a celebrated result of Kawahigashi, Longo, and
Mueger:
The representation category of a conformal net (subject to appropriate finiteness conditions) is a modular tensor category.
All this is related to my ongoing research projects with Chris Douglas and Arthur Bartels, in which we investigate conformal nets from a category
theoretical
perspective.