Discusses fundamental problems and results of the theory of random matrices, and their connections to tools of algebra and combinatorics: Wigner's semicircle law, free probability, Gaussian, circular, and beta ensembles …
This course studies real variable methods for singular integrals and related functional spaces.
Applies functional analysis to physical problems; scattering theory, statistical mechanics, and quantum field theory.
Studies selected topics in algebraic or analytic number theory
This course provides the opportunity to offer a new topic in the subject of mathematics.
The foundations of commutative algebra, algebraic number theory, or algebraic geometry.
Studies the foundations of algebraic geometry.
Theory of number fields and local fields, ramification theory, further topics as chosen by instructor.
Studies basic results concerning Lie groups, Lie algebras, and the correspondence between them.
Studies basic structure theory of Lie algebras.
Studies differential geometry in the large; connections; Riemannian geometry; Gauss-Bonnet formula; and differential forms.
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.
Selected advanced topics in algebraic topology.
Studies the basic structure theory of groups, especially finite groups.
Studies the foundations of representation and character theory of finite groups.
Covers methods of abstract algebra that can be applied to various combinatorial problems and combinatorial methods to approach problems in representation theory, algebraic geometry, and homological algebra.
Studies the basic structure theory of associative or nonassociative algebras.
Studies groups of transformations operating on a space; properties of fixed-point sets, orbit spaces; and local and global invariants.
For master's research, taken before a thesis director has been selected.
For master's thesis, taken under the supervision of a thesis director.