Title: Toda Conformal Field Theories: between probability, geometry and vertex algebras
Speaker: Baptiste Cerclé（Sorbonne University, Paris.）
Time: June 22 (Monday), June 23 (Tuesday)，June 24 (Wednesday) 2026, 09:30-11:30
Venue：Gewu Building 315
Abstract:
Toda theories form a family of two-dimensional Conformal Field Theories that generalize the celebrated Liouville theory. Initially introduced in the physics literature, their mathematical study involves many very active areas of research, ranging from probability theory to algebraic and conformal geometry or representation theory of vertex algebras. The goal of this minicourse will be to explain the probabilistic construction of such theories and show that it provides a unified framework where algebraic and geometric perspectives can be gathered.
About the speaker: Baptiste Cerclé is a CNRS researcher at Sorbonne Université’s Laboratoire de Physique Théorique et Hautes Energies (LPTHE). He studied at the École Normale Supérieure de Lyon and obtained his PhD from Université Paris-Saclay in 2023. He then held a postdoctoral position at EPFL and has given invited talks at major institutions worldwide, including the Hausdorff Institute, CIRM, Peking University and the Bernoulli Center. He is internationally recognized for his pioneering work on Toda conformal field theories — a rich family of two-dimensional CFTs that generalize Liouville quantum gravity. His work heavily relies on tools from probability theory, representation theory, and vertex operator algebras. His recent publications appear in top journals such as the Journal of the European Mathematical Society, Communications in Mathematical Physics, and the Proceedings of the London Mathematical Society.
