Mathematics

This course covers current topics in Number Theory and Related Analysis. Specific topic information provided when course is taught.

This course covers current topics in Algebraic Number Theory. More specific topic details provided when the course is taught.

This course covers current topics in Arithmetic Number Theory. Specific topic information provided when course is offered.

This course covers current topics in Automorphic Forms. Specific topic information provided when the course is taught.

This course covers current topics in number theory. Specific topic information will be provided when the course is offered.

Basic introductory course to modern methods of analysis. Specific applications of methods to problems in other fields, such as partial differential equations, probability, & number theory are presented. Topics include Lp spaces, tempered distribution, Fourier transform, Riesz interpolation theorem, Hardy-Littlewood maximal function, Calderon-Zygmund theory, the spaces H1 and BMO, oscillatory integrals, almost orthogonality, restriction theorems & applications to dispersive equations, law of large numbers & ergodic theory. Course also discusses applications of Fourier methods to discrete counting problems, using Poisson summation formula.

The course is a basic introductory graduate course in partial differential equations. Topics include: Laplacian, properties of harmonic functions, boundary value problems, wave equation, heat equation, Schrodinger equation, hyperbolic conservation laws, Hamilton-Jacobi equations, Fokker-Planck equations, basic function spaces and inequalities, regularity theory for second order elliptic linear PDE, De Giorgi method, basic harmonic analysis methods, linear evolution equations, existence, uniqueness and regularity results for classes of nonlinear PDE with applications to equations of nonlinear and statistical physics.

This course covers current topics in Harmonic Analysis. More specific topic information is provided when the course is offered.

This course covers current topics in Geometric Analysis and General Relativity. More specific topic details provided when the course is offered.

This course covers current topics in Differential Geometry. (More details provided the course is offered/scheduled.)

This course covers current topics in Nonlinear Analysis. More specific details will be provided when the course is offered.

This course covers current topics in Analysis. Specific topic details provided when offered.

This course is an introduction to the theory of compact Riemann surfaces, including some basic properties of the topology of surfaces, differential forms and the basis existence theorems, the Riemann-Roch theorem and some of its consequences, and the general uniformization theorem if time permits.

This course covers current topics in Algebraic Geometry. Specific topic details provided when course is offered.

This course covers current topics in Algebra. More specific topic details provided when the course is offered.

This is an introductory graduate course covering questions and methods in differential geometry. As time permits, more specialized topics will be covered as well, including minimal submanifolds, curvature and the topology of manifolds, the equations of geometric analysis and its main applications, and other topics of current interest.

This course covers current topics in differential geometry. Specific topic information will be provided when the course is offered.

This course covers current topics in Conformal and Cauchy-Rieman (CR) Geometry. More specific topic details are provided when the course is offered.

This course covers current topics in Geometry. More specific topic details provided when course is offered.

The aim of the course is to study some of the basic algebraic techniques in Topology, such as homology groups, cohomology groups and homotopy groups of topological spaces.

This course covers current topics in Differential Topology. More specific topic details provided when the course is offered.

This course covers current topics in Low Dimensional Topology. Specific topic information provided when the course is taught.

Knot theory involves the study of smoothly embedded circles in three-dimensional manifolds. There are lots of different techniques to study knots: combinatorial invariants, algebraic topology, hyperbolic geometry, Khovanov homology and gauge theory. This course will cover some of the modern techniques and recent developments in the field.

This course covers current topics in Topology. More specific topic details provided when the course is offered.

This course covers current topics in combinatorial optimization. More specific topic details are provided when the course is offered.