MATH-680: Monstrous moonshine

Lectures in this course (11)

Explores Weyl characters, Macdonald's identities, and Borcherds products in Euclidean space.

Explores the construction of the Fischer-Greiss monster group, emphasizing its key properties and the process involved.

Explores the Monster group, a sporadic simple group with a unique representation theory.

Delves into Macdonald identities, covering affine root systems, modular forms, and Lie algebras.

Explores Monstrous Moonshine, focusing on the 1979 discovery and its mathematical connections.

Explores Borcherds' proof strategy for monstrous moonshine and Lie superalgebras.

Covers Borcherds' proof strategy, emphasizing the significance of simple roots and Weyl vectors.

Explores harmonic forms on Riemann surfaces, covering uniqueness of solutions and the Riemann bilinear identity.

Covers the basics of Vertex Operator Algebras, including normal ordering, fields, and product fields.

Explores conformal vectors, Virasoro algebra, and Heisenberg vertex algebra in the theory of vertex operator algebras.

Explores the proof of the Weyl character formula for finite-dimensional representations of semisimple Lie algebras.

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