Speaker: Bin Gui 归斌 (Tsinghua University)
Time: Tues., 10:00-11:30 am, March 10, 2026
Place: Room 102, No.1 Teaching Building. 清华大学 一教 102
Title: Conformal blocks and associative algebras in logarithmic conformal field theory
Abstract: A main theme in the development of the theory of vertex operator algebras (VOAs) is the factorization property. If $V$ is a $C_2$-cofinite rational VOA (which corresponds to the chiral algebra of a rational CFT in physics), the factorization property---saying roughly that higher genus conformal blocks can be decomposed into lower genus ones---was recently completely proved. Its low genus special cases (such as Zhu's modular invariance theorem in 1996 and Huang's associativity theorem for intertwining operators in 2005) are crucial to the understanding of the representation theory of $V$.
This talk focuses on $C_2$-cofinite VOAs that are not necessarily rational. Such VOAs correspond to chiral algebras of finite-type logarithmic CFTs. Since their representation categories are not necessarily semisimple, the study of their conformal blocks differ significantly from the rational case. In this talk, I will present my recent joint work with Hao Zhang on the complete proof of the factorization property for conformal blocks of such VOAs. We will also discuss the natural associative algebras in log CFT that play the role of Zhu's algebra in rational CFT. In particular, we show that the 0-th order Hochschild cohomology of that algebra is isomorphic to the space of torus conformal blocks. This is based on our works arXiv:2503.23995 and arXiv:2508.04532.
Time: Dec 30, 10:00-12:00
Place: Teaching Building No.1, Room 102. Tsinghua
Title: Higher chiral algebras and free field realizations
Speaker: Zhengping Gui (SIMIS and Fudan U.)
Abstract: We use the Jouanolou model as a model for configuration spaces to construct higher-dimensional chiral algebras. In this model, chiral algebras can be studied as homotopy Lie algebras within a pseudotensor structure. Parallel to the standard complex one-dimensional case, free field realizations provide a useful tool and offer access to studying explicit expressions for higher-dimensional Virasoro and Kac-Moody central extensions. This is a joint work with Minghao Wang and Brian Williams.
Speaker: Miquel Cueca (KU Leuven)
Time: Oct 21, 2025 10:00-11:30 am
Place: Room 204, No.1 Teaching Building. 清华大学 一教 204
Title: Dimensional reduction for Manin triples
Abstract: A Manin triple for a Courant algebroid consists of a pair of transverse Dirac structures. We will prove that the Courant sigma model on a closed surface times the interval and boundary conditions in one of Dirac structures admits a gauge fixing leading, on the closed surface, to the Poisson sigma model of the Poisson groupoid integrating the second Dirac structure. This is a joint work with Alejandro Cabrera.
Speaker: Anton Alexeev (Université de Genève)
Time: Oct 14,2025 10:00-11:30 am
Location: No. 6, Teaching Building 六教 6A103
Title: Teichmüller spaces for surfaces with boundary, and Virasoro algebra
Abstract:
Teichmüller spaces associated to closed oriented surfaces carry Weil-Petersen symplectic structures which admit many descriptions. In particular, by the results of Goldman and Hitchin, these Teichmüller spaces are connected components of moduli spaces of flat connections which carry Atiyah-Bott symplectic forms, and they admit explicit Fenchel-Nielsen Darboux coordinates.
In this talk, we consider infinite dimensional Teichmüller spaces associated to oriented surfaces with absolute boundary. We show that similarly to their finite dimensional counterparts they carry canonical symplectic forms. Suprizingly, they also carry Hamiltonian actions of the Virasoro algebra.
This work is motivated by recent works on Jackiw-Teitelboim 2-dimensional gravity, and by the study of moduli of flat connections for surfaces with boundary. The talk is based on a joint work with E. Meinrenken, see arXiv:2401.03029, and on a work in progress with R. Dalipi and S. Shatashvili.
