Graduate Courses

Spring 2019

Algebraic Topology
AS.110.616 (01)

Polyhedra, simplicial and singular homology theory, Lefschetz fixed-point theorem, cohomology and products, homological algebra, Künneth and universal coefficient theorems, Poincar&ecute; and Alexander duality theorems.

Credits: 0.00
Level: Graduate
Status: Open
Seats Available: 10/15
PosTag(s): n/a

Algebra
AS.110.602 (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, and rudiments of category theory, homological algebra, field theory, Galois theory, and non-commutative algebras. Recommended Course Background: AS.110.401-AS.110.402

Credits: 0.00
Level: Graduate
Status: Open
Seats Available: 11/15
PosTag(s): n/a

Algebraic Geometry
AS.110.644 (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, schemes, connections with complex analytic geometry and topology.

Credits: 0.00
Level: Graduate
Status: Open
Seats Available: 8/10
PosTag(s): n/a

Partial Differential Equations I
AS.110.631 (01)

An introductory graduate course in partial differential equations. Classical topics include first order equations and characteristics, the Cauchy-Kowalewski theorem, Laplace’s equations, heat equation, wave equation, fundamental solutions, weak solutions, Sobolev spaces, maximum principles.

Credits: 0.00
Level: Graduate
Status: Open
Seats Available: 13/15
PosTag(s): n/a

Lie Groups and Lie Algebras
AS.110.619 (01)

Lie groups and Lie algebras, classification of complex semi-simple Lie algebras, compact forms, representations and Weyl formulas, symmetric Riemannian spaces.

Credits: 0.00
Level: Graduate
Status: Open
Seats Available: 2/15
PosTag(s): n/a

Complex Variables
AS.110.607 (01)

Analytic functions of one complex variable. Topics include Mittag-Leffler Theorem, Weierstrass factorization theorem, elliptic functions, Riemann-Roch theorem, Picard theorem, and Nevanlinna theory. Recommended Course Background: AS.110.311, AS.110.405

Credits: 0.00
Level: Graduate
Status: Open
Seats Available: 8/15
PosTag(s): n/a

Riemannian Geometry
AS.110.646 (01)

The goal is to give a self-contained course on mean curvature flow, starting with the basic linear heat equation in Euclidean space and – hopefully – getting to topics of current research. Mean curvature flow is a geometric heat equation that shares many properties with Ricci flow, harmonic map heat flow, Yang-Mills flow and the Navier-Stokes equations. Recommended Course Background: AS.110.605 and an undergraduate course in differential geometry; AS.110.645 and AS.110.631

Credits: 0.00
Level: Graduate
Status: Open
Seats Available: 7/15
PosTag(s): n/a

Number Theory
AS.110.618 (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, semi-simple algebras over local and number fields, adele geometry.

Credits: 0.00
Level: Graduate
Status: Canceled
Seats Available: 15/15
PosTag(s): n/a

Harmonic Analysis
AS.110.633 (01)

Fourier multipliers, oscillatory integrals, restriction theorems, Fourier integral operators, pseudodifferential operators, eigenfunctions. Undergrads need instructor's permission.

Credits: 0.00
Level: Graduate
Status: Open
Seats Available: 7/15
PosTag(s): n/a

Topics in Analysis
AS.110.726 (01)

The topics covered will involve the theory of calculus of Functors applied to Geometric problems like Embedding theory. Other related areas will be covered depending on the interest of the audience.

Credits: 0.00
Level: Graduate
Status: Open
Seats Available: 6/12
PosTag(s): n/a

Topics In Alg Num Theory
AS.110.733 (01)

Credits: 0.00
Level: Graduate
Status: Open
Seats Available: 7/12
PosTag(s): n/a

Thesis Research
AS.110.801 (01)

Credits: 0.00
Level: Graduate
Status: Open
Seats Available:
PosTag(s): n/a

Thesis Research
AS.110.801 (11)

Credits: 0.00
Level: Graduate
Status: Open
Seats Available:
PosTag(s): n/a

Seminar in Number Theory
AS.110.798 (01)