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In this 55-minute lecture, Antti Kupiainen continues his exploration of Probabilistic Conformal Field Theory in Part 2 of the series from the Hausdorff Center for Mathematics. Delve into the mathematical foundations of Conformal Field Theories (CFTs), which describe universal behavior of physical systems at second order phase transition points and play crucial roles in Quantum Field Theories. Learn about the probabilistic approach to CFT based on path integral formulation and its connection to Graeme Segal's geometric approach to conformal bootstrap. Explore two prominent CFTs in detail: the Liouville CFT, central to Liouville Quantum Gravity and random surfaces theory, and the Wess-Zumino-Witten models with their rich representation theoretical content. Discover how these mathematical structures, first uncovered by physicists Belavin, Polyakov, and Zamolodchicov in 1983, continue to have profound impacts on representation theory and geometry despite ongoing debates about their rigorous mathematical foundations.
