A biased introduction to two-dimensional conformal field theoryMPIM

by Aaron Hofer (MPIM)

Thursday Feb 26, 2026, 3:00 PM → 4:00 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Lecture Hall (Max Planck Institute for Mathematics)

MPI-Oberseminar

Two dimensional conformal field theories (CFTs) are one of the most well studied classes of quantum field theories, with applications ranging from string theory to critical systems in statistical physics. Moreover, their rich symmetry structure allows for a rigorous mathematical treatment leading to connections between several, distinct mathematical disciplines including complex analysis, probability theory, algebraic geometry, number theory, quantum topology, and representation theory.
In this talk I will give an overview of one particular approach to understand and 'classify' the class of so-called rational CFTs using vertex operator algebras and three-dimensional topological field theories. In the end I will also comment on work in progress on how to extend this programme beyond the rational setting.