In critical phenomena, it is well known that a system at the critical point exhibits conformal invariance. A field theory with this symmetry is called a conformal field theory (CFT). In particular, in two-dimensional spacetime, the generators of conformal transformations form an infinite-dimensional Lie algebra known as the Virasoro algebra, and this infinite-dimensional symmetry enables a systematic classification of critical phenomena. Two-dimensional conformal field theory has had a major impact not only on physical applications such as critical phenomena and string theory, but also on mathematics, including representation theory.

In this lecture, I will focus on the representation theory of the Virasoro algebra and minimal models.