Lectures related to Borcherds' Proof: Strategy

Differential Forms on Manifolds

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

Monstrous Moonshine

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

Fundamental Groups

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

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Proper Actions and Quotients

Covers proper actions of groups on Riemann surfaces and introduces algebraic curves via square roots.

Group Theory in Physics

Covers the fundamentals of group theory in physics, focusing on symmetries and transformations leaving physical equations unchanged.

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Harmonic Forms: Main Theorem

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Lie Algebra: Group Theory

Explores Lie Algebra's connection to Group Theory through associative operations and Jacobi identities.

Lie Groups: Representations and Transformations

Explores Lie groups, scalar fields, and vector spaces transformations.

Bar Construction: Homology Groups and Classifying Space

Covers the bar construction method, homology groups, classifying space, and the Hopf formula.

Local structure of totally disconnected locally compact groups III

Explores the local structure of totally disconnected locally compact groups and their isomorphisms through conjugation.

Isometries and Group Homomorphisms

Explores isometries, group homomorphisms, linear transformations, and group generation by similarities.

Differential Forms Integration

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Local structure of totally disconnected locally compact groups II

Explores the local structure of totally disconnected locally compact groups, covering commensurated subgroups, completions, local automorphisms, and the quasi-centre.

Decomposition of Group Algebras

Covers examples of group algebra decomposition and simple infinite-dimensional algebras.

Conformal Maps and Hyperbolic Geometry

Explores conformal maps, hyperbolic geometry, and isometric properties of disks.

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Local structure of totally disconnected locally compact groups I

Covers the local structure of totally disconnected locally compact groups, exploring properties and applications.

Symmetries and Groups in Quantum Mechanics

Covers the role of symmetries and groups in quantum mechanics, focusing on SU2 and SU3, their properties, and implications for physical theories.