Devoted to chomology theory: cohomology groups, the universal coefficient theorem, the Kunneth formula, cup products, the cohomology ring of manifolds, Poincare duality, and other topics if time permits. Prerequisite: MATH …
Topics include smooth manifolds and functions, tangent bundles and vector fields, embeddings, immersions, transversality, regular values, critical points, degree of maps, differential forms, de Rham cohomology, and connections. Prerequisite: MATH …
Examines fiber bundles; induced bundles, principal bundles, classifying spaces, vector bundles, and characteristic classes, and introduces K-theory and Bott periodicity. Prerequisite: MATH 7800.
Definition of homotopy groups, homotopy theory of CW complexes, Huriewich theorem and Whitehead's theorem, Eilenberg-Maclane spaces, fibration and cofibration sequences, Postnikov towers, and obstruction theory. Prerequisite: MATH 7800.
Studies algebraic properties of RNA secondary structures, primarily using techniques from algebraic topology and homological algebra.
Theory of distributions. Sobolev spaces and their properties (trace and embedding theorems). Theory of elliptic equations. Time-dependent partial differential equations: parabolic and hyperbolic equations. Topics in nonlinear partial differential equations. …
Topics in the theory of operators on a Hilbert space and related areas of function theory.
Topics in the theory of operators on a Hilbert space and related areas of function theory.
This course presents the basic theory of stochastic differential equations and provides examples of its applications. It is an essential topic for students preparing to do research in probability. Topics …
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 …