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Quasiconformal Teichmüller theory as an analytical foundation for two-dimensional conformal field theor
Aalto Univ, Dept Math & Syst Anal, Aalto, Finland.
Univ Manitoba, Dept Math, Winnipeg, Canada.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
2017 (English)In: Lie Algebras, Vertex Operator Algebras, And Related Topics / [ed] Barron, Katrina; Jurisich, Elizabeth; Milas, Antun & Misra, Kailash, American Mathematical Society (AMS), 2017, p. 205-238Conference paper, Published paper (Refereed)
Abstract [en]

The functorial mathematical definition of conformal field theory was first formulated approximately 30 years ago. The underlying geometric category is based on the moduli space of Riemann surfaces with parametrized boundary components and the sewing operation. We survey the recent and careful study of these objects, which has led to significant connections with quasiconformal Teichmuller theory and geometric function theory. In particular we propose that the natural analytic setting for conformal field theory is the moduli space of Riemann surfaces with so-called WeilPetersson class parametrizations. A collection of rigorous analytic results is advanced here as evidence. This class of parametrizations has the required regularity for CFT on one hand, and on the other hand are natural and of interest in their own right in geometric function theory.

Place, publisher, year, edition, pages
American Mathematical Society (AMS), 2017. p. 205-238
Series
Contemporary Mathematics, ISSN 0271-4132 ; 695
National Category
Geometry
Identifiers
URN: urn:nbn:se:uu:diva-358118DOI: 10.1090/conm/695/14003ISI: 000431843300013ISBN: 978-1-4704-2666-8 (print)OAI: oai:DiVA.org:uu-358118DiVA, id: diva2:1241829
Conference
International Conference on Lie Algebras, Vertex Operator Algebras, and Related Topics, AUG 14-18, 2015, Univ Notre Dame, Notre Dame, IN
Funder
The Wenner-Gren FoundationAvailable from: 2018-08-24 Created: 2018-08-24 Last updated: 2018-08-24Bibliographically approved

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Staubach, Wolfgang

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