主讲人 / Speaker
Tomáš Procházka
Institute of Physics of the Czech Academy of Sciences
时间 / Time
Thursday, 13:30-15:05, Dec. 11, 2025;
Monday, 9:50-11:25 am, Dec. 15, 2025
地点 / Venue
Lecture 1: B627, Dec 11, 13:30-15:05
Lecture 2: B541, Dec 15, 9:50-11:25 am
Shuangqing Complex Building
ODE/IM correspondence and W-algebras
课程介绍 / Description
As is well known, the 2d conformal field theories are governed by the Virasoro algebra. Higher spin extensions of Virasoro algebra are called W-algebras. It is interesting to study these algebraic structures from the point of view of quantum integrability and the associated Yangian structures.
ODE/IM correspondence relates the spectrum of an infinity family of commuting conserved quantities to study of ordinary differential equations in the complex domain. WKB expansion of the wave function allows to extract eigenvalues of the commuting Hamiltonians in terms of the geometry of the associated WKB curve. The aim of these lectures is to make a basic introduction to these topics.
主讲人简介 / About the Speaker
My primary research focus is on two-dimensional conformal field theory with higher-spin symmetries. Quantum field theories in two spacetime dimensions that exhibit additional invariance under conformal transformations represent a remarkable class of theories, many of which are exactly solvable. This solvability arises from their infinite-dimensional symmetry algebra, known as the Virasoro algebra. By extending the spacetime symmetry transformations to include higher-spin transformations, one can explore even larger symmetry algebras.
While a clear geometric interpretation of these extended symmetries remains elusive, their algebraic structure reveals fascinating connections to various areas of mathematical physics. For instance, these symmetry algebras govern the properties of supersymmetric BPS states in four-dimensional quantum gauge theories, with or without conformal symmetry. They are also intricately linked to the integrable structures in exactly solvable models, such as Calogero systems, and feature in various string theory constructions, including topological strings and the holographic duality proposed by Eberhardt, Gaberdiel, and Gopakumar.
Speaker website:
//p4f.fzu.cz/fzu_supervisor/tomas-prochazka-ph-d/
