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Lie Group Quantum Mathematics Seminar

Conformal bootstrap and Segal axioms for Liouville Conformal Field Theory

Guillarmou Colin (Universite Paris-Saclay)

Location:  Hill Center Room 705 and on Zoom
Date & time: Tuesday, 03 May 2022 at 2:00PM - 3:00PM

Abstract In this talk, I will review recent works done in collaboration with Kupiainen, Rhodes and Vargas on the Liouville conformal field theory (CFT).  This two dimensional CFT is a theory of random Riemannian surfaces introduced and intensely studied in physics since the 80s. We use a probabilistic approach to define the path integral and we combine these probabilistic tools with scattering theory to give a mathematical proof of the so called "conformal bootstrap". This allows us to express the n-point correlation functions on all surfaces in terms of conformal blocks and structure constants. This approach also gives a rigorous definition of the conformal blocks as converging series in the moduli parameters for this CFT.

Zoom link
Meeting ID: 939 2146 5287
Passcode: 196884, the dimension of the weight 2 homogeneous
subspace of the moonshine module

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