Linear Algebra

The purpose of the course is to introduce the basic notions of linear algebra and its applications.

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Lie Algebras

We introduce finite dimensional semisimple complex Lie algebras and establish the classification theorem.

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Representation theory of semisimple lie algebras

We will establish the major results in the representation theory of semisimple Lie algebras over the field of complex numbers, and that of the related algebraic groups.

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Topics in the theory of reductive algebraic groups, Lie algebras, and representation theory I (2019)

The topics addressed in this course are the structure theory of eductive algebraic groups, their associated Lie algebras, the related finite groups of Lie type, and the representation theory of all of these objects.

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Topics in the theory of reductive algebraic groups, Lie algebras, and representation theory II

The topics addressed in this course are the structure theory of eductive algebraic groups, their associated Lie algebras, the related finite groups of Lie type, and the representation theory of all of these objects.

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