Course Descriptions

Graduate Course Descriptions

Lie Algebras (3.00)

MATH 8710

Studies basic structure theory of Lie algebras.

Differential Geometry (3.00)

MATH 8720

Studies differential geometry in the large; connections; Riemannian geometry; Gauss-Bonnet formula; and differential forms.

Topology of Manifolds (3.00)

MATH 8750

Studies regular and critical values, gradient flow, handle decompositions, Morse theory, h-cobordism theorem, Dehn's lemma in dimension 3, and disk theorem in dimension 4. Prerequisite: Math 5770.

Generalized Cohomology Theory (3.00)

MATH 8800

Topics include the axiomatic generalized cohomology theory; representability and spectra; spectra and ring spectra; orientability of bundles in generalized cohomology theory; Adams spectral sequence, and stable homotopy.

Cobordism and K-Theory (3.00)

MATH 8830

Studies classical cobordism theories; Pontryagin-Thom construction; bordism and cobordism of spaces; K-theory and Bott periodicity; formal groups, and cobordism.

Topics in Algebraic Topology (3.00)

MATH 8850

Selected advanced topics in algebraic topology.

Group Theory (3.00)

MATH 8851

Studies the basic structure theory of groups, especially finite groups.

Representation Theory (3.00)

MATH 8852

Studies the foundations of representation and character theory of finite groups.

Algebraic Combinatorics (3.00)

MATH 8853

Studies geometries, generating functions, partitions, and error-correcting codes and graphs using algebraic methods involving group theory, number theory, and linear algebra.

Arithmetic Groups (3.00)

MATH 8854

General methods of analyzing groups viewed as discrete subgroups of real algebraic subgroups. Additional topics include the congruence subgroup problem. Prerequisite: MATH 7752.

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