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Conformal Field Theory is a branch of physics with origins in solvable lattice models and string theory. But the mathematics that it has inspired has many applications in pure mathematics.nWe will give an introduction to this theory with related representation theories of the Virasoro and affine Lie algebras, and vertex operators.nnPrerequisites: we will not assume any particular knowledge from physics, but some knowledge of Lie algebras will be helpful.nnNOTE: Undergraduates require instructor permission to enroll. Undergraduates interested in taking the course should contact the instructor for permission, providing information about relevant background such as performance in prior coursework, reading, etc.nnnMay be repeated for credit.