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IN-PERSON MATHEMATICAL PHYSICS SEMINAR
RUTGERS UNIVERSITY
HILL 705
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Special joint Lie Group/Quantum Math Seminar and Mathematical Physics Seminar
Guillarmou Colin - Universite Paris-Saclay
Date/Time/Location
Tuesday, May 3rd, 2:00pm; Hill Center 705
"Conformal bootstrap and Segal axioms for Liouville Conformal Field Theory"
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.