Column one has the course number and section. Other columns show the course title, days offered, instructor's name, room number, if the course is cross-referenced with another program, and a option to view additional course information in a pop-up window.
Course # (Section)
Title
Day/Times
Instructor
Room
Info
AS.110.605 (01)
Real Variables
MW 12:00PM - 1:15PM
Sogge, Christopher
Real Variables AS.110.605 (01)
Measure and integration on abstract and locally compact spaces (extension of measures, decompositions of measures, product measures, the Lebesgue integral, differentiation, Lp-spaces); introduction to functional analysis; integration on groups; Fourier transforms.
Credits: 4.00
Level: Graduate
Days/Times: MW 12:00PM - 1:15PM
Instructor: Sogge, Christopher
Room:
Status: Open
Seats Available: 3/20
AS.110.645 (01)
Riemannian Geometry
TTh 10:30AM - 11:45AM
Bernstein, Jacob
Riemannian Geometry AS.110.645 (01)
Differential manifolds, vector fields, flows, Frobenius’ theorem. Differential forms, deRham’s theorem, vector bundles, connections, curvature, Chern classes, Cartan structure equations. Riemannian manifolds, Bianchi identities, geodesics, exponential maps. Geometry of submanifolds, hypersurfaces in Euclidean space. Other topics as time permits, e.g., harmonic forms and Hodge theorem, Jacobi equation, variation of arc length and area, Chern-Gauss-Bonnet theorems.
Credits: 4.00
Level: Graduate
Days/Times: TTh 10:30AM - 11:45AM
Instructor: Bernstein, Jacob
Room:
Status: Open
Seats Available: 9/20
AS.110.601 (01)
Algebra
TTh 12:00PM - 1:15PM
Shokurov, Vyacheslav
Algebra AS.110.601 (01)
An introductory graduate course on fundamental topics in algebra to provide the student with the foundations for number theory, algebraic geometry, and other advanced courses. Topics include group theory, commutative algebra, Noetherian rings, local rings, modules, rudiments of category theory, homological algebra, field theory, Galois theory, and non-commutative algebras.
Credits: 4.00
Level: Graduate
Days/Times: TTh 12:00PM - 1:15PM
Instructor: Shokurov, Vyacheslav
Room:
Status: Open
Seats Available: 15/20
AS.110.608 (01)
Riemann Surfaces
MW 12:00PM - 1:15PM
Mese, Chikako
Riemann Surfaces AS.110.608 (01)
Abstract Riemann surfaces. Examples: algebraic curves, elliptic curves and functions on them. Holomorphic and meromorphic functions and differential forms, divisors and the Mittag-Leffler problem. The analytic genus. Bezout's theorem and applications. Introduction to sheaf theory, with applications to constructing linear series of meromorphic functions. Serre duality, the existence of meromorphic functions on Riemann surfaces, the equality of the topological and analytic genera, the equivalence of algebraic curves and compact Riemann surfaces, the Riemann-Roch theorem. Period matrices and the Abel-Jacobi mapping, Jacobi inversion, the Torelli theorem. Uniformization (time permitting).
Credits: 0.00
Level: Graduate
Days/Times: MW 12:00PM - 1:15PM
Instructor: Mese, Chikako
Room:
Status: Open
Seats Available: 4/15
AS.110.615 (01)
Algebraic Topology I
MW 10:30AM - 11:45AM
Kitchloo, Nitya
Algebraic Topology I AS.110.615 (01)
Polyhedra, simplicial and singular homology theory, Lefschetz fixed-point theorem, cohomology and products, homological algebra, Künneth and universal coefficient theorems, Poincaré and Alexander duality theorems.
Credits: 4.00
Level: Graduate
Days/Times: MW 10:30AM - 11:45AM
Instructor: Kitchloo, Nitya
Room:
Status: Open
Seats Available: 10/20
AS.110.617 (01)
Number Theory
TTh 10:30AM - 11:45AM
Consani, Caterina
Number Theory AS.110.617 (01)
Topics in advanced algebra and number theory, including local fields and adeles, Iwasawa-Tate theory of zeta functions and connections with Hecke’s treatment, semisimple algebras over local and number fields, adeles geometry.
Credits: 0.00
Level: Graduate
Days/Times: TTh 10:30AM - 11:45AM
Instructor: Consani, Caterina
Room:
Status: Open
Seats Available: 14/20
AS.110.632 (01)
Partial Differential Equations II
TTh 1:30PM - 2:45PM
Dodson, Benjamin
Partial Differential Equations II AS.110.632 (01)
An introductory graduate course in partial differential equations. Classical topics include first order equations and characteristics, the Cauchy-Kowalevski theorem, Laplace's equation, heat equation, wave equation, fundamental solutions, weak solutions, Sobolev spaces, maximum principles. The second term focuses on special topics such as second order elliptic theory.
Credits: 0.00
Level: Graduate
Days/Times: TTh 1:30PM - 2:45PM
Instructor: Dodson, Benjamin
Room:
Status: Open
Seats Available: 15/20
AS.110.637 (01)
Functional Analysis
MW 12:00PM - 1:15PM
Lindblad, Hans
Functional Analysis AS.110.637 (01)
Credits: 0.00
Level: Graduate
Days/Times: MW 12:00PM - 1:15PM
Instructor: Lindblad, Hans
Room:
Status: Open
Seats Available: 18/30
AS.110.643 (01)
Algebraic Geometry
TTh 9:00AM - 10:15AM
Han, Jingjun
Algebraic Geometry AS.110.643 (01)
Affine varieties and commutative algebra. Hilbert’s theorems about polynomials in several variables with their connections to geometry. General varieties and projective geometry. Dimension theory and smooth varieties. Sheaf theory and cohomology. Applications of sheaves to geometry; e.g., the Riemann-Roch theorem. Other topics may include Jacobian varieties, resolution of singularities, geometry on surfaces, connections with complex analytic geometry and topology, schemes.
