## Vertex Operator Algebras: Theory, Examples, and Problems

Vertex operator algebras are a mathematical approach to two-dimensional chiral conformal field theory. In these talks, I will introduce the definition of vertex operator algebra with motivation from the Segal picture of conformal field theory and discuss examples coming from the Virasoro algebra, affine Lie algebras, and lattices. Where possible, I will indicate connections with more analytic approaches to conformal field theory. Further topics will include tensor structures on representations of vertex operator algebras, major open problems in the field, and, time permitting, some of my work on tensor categories of affine Lie algebra representations and vertex operator algebra extensions.

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