Graduate Courses

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.

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)

Presentations of current research papers by faculty, graduate students and invited guest speakers. For graduate students only.

  • Credits: 0.00
  • Level: Graduate
  • Status: Canceled
  • Seats Available: 35/35
  • PosTag(s): n/a

Seminar in Category Theory
AS.110.794 (01)

Presentations of current research papers by faculty, graduate students and invited guest speakers. For graduate students only.

  • Credits: 0.00
  • Level: Graduate
  • Status: Canceled
  • Seats Available: 25/25
  • PosTag(s): n/a

Seminar in Algebraic Geometry
AS.110.799 (01)

For graduate students only. Presentations of current research papers by faculty, graduate students and invited guest speakers.

  • Credits: 0.00
  • Level: Graduate
  • Status: Canceled
  • Seats Available: 35/35
  • PosTag(s): n/a

Seminar in Analysis and Partial Differential Equations
AS.110.791 (01)

Presentations of current research papers by faculty, graduate students and invited guest speakers. For graduate students only.

  • Credits: 0.00
  • Level: Graduate
  • Status: Canceled
  • Seats Available: 35/35
  • PosTag(s): n/a

Topics in Stochastic Dynamical Systems
AS.110.757 (01)

The course will present an introduction to stochastic dynamical systems and some applications in model reduction and data assimilation. The main focus will be on stability and ergodicity of stochastic dynamical systems, including stochastic differential equations driven by white and fractional noise, and their numerical approximations. We will then discuss model reduction, focusing on Mori-Zwanzig formalism and approximation of the generalized Langevin equation, and methods on the parametric inference of related stochastic systems. Data assimilation and stochastic control will also be briefly introduced.

  • Credits: 0.00
  • Level: Graduate
  • Status: Open
  • Seats Available: 3/12
  • PosTag(s): n/a

Seminar in Complex Geometry
AS.110.790 (01)

Presentations of current research papers by faculty, graduate students and invited guest speakers. For graduate students only.

  • Credits: 0.00
  • Level: Graduate
  • Status: Canceled
  • Seats Available: 35/35
  • PosTag(s): n/a

Topics:Partial Differential Equations
AS.110.741 (01)

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

Data Science Seminar
AS.110.795 (01)

Presentations of current research papers by faculty, graduate students and invited guest speakers. For graduate students only.

  • Credits: 0.00
  • Level: Graduate
  • Status: Canceled
  • Seats Available: 45/45
  • PosTag(s): n/a

Seminar in Topology
AS.110.793 (01)

For graduate students only. Presentations of current research papers by faculty, graduate students and invited guest speakers.

  • Credits: 0.00
  • Level: Graduate
  • Status: Canceled
  • Seats Available: 35/35
  • PosTag(s): n/a

Thesis Research
AS.110.801 (05)

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

Thesis Research
AS.110.801 (04)

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

Thesis Research
AS.110.801 (06)

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

Thesis Research
AS.110.801 (07)

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

Thesis Research
AS.110.801 (09)

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

Thesis Research
AS.110.801 (10)

  • Credits: 0.00
  • Level: Graduate
  • Status: Open
  • Seats Available: 5/5
  • PosTag(s): n/a

Thesis Research
AS.110.801 (08)

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

Thesis Research
AS.110.801 (03)

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

Thesis Research
AS.110.801 (02)

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

Thesis Research
AS.110.801 (12)

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

Thesis Research
AS.110.801 (14)

  • Credits: 0.00
  • Level: Graduate
  • Status: Open
  • Seats Available: 5/5
  • PosTag(s): n/a

Thesis Research
AS.110.801 (13)

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

Course # (Section) Title Day/Times Instructor Room PosTag(s) Info
AS.110.616 (01)Algebraic TopologyTTh 10:30AM - 11:45AMKitchloo, NityaKrieger 308
AS.110.602 (01)AlgebraMW 12:00PM - 1:15PMShokurov, VyacheslavBloomberg 276
AS.110.644 (01)Algebraic GeometryTTh 10:30AM - 11:45AMStaffKrieger 204
AS.110.631 (01)Partial Differential Equations IMW 12:00PM - 1:15PMWang, YiBloomberg 178
AS.110.619 (01)Lie Groups and Lie AlgebrasTTh 9:00AM - 10:15AMZheng, XudongKrieger 204
AS.110.607 (01)Complex VariablesTTh 10:30AM - 11:45AMSpruck, JoelBloomberg 172
AS.110.646 (01)Riemannian GeometryMW 1:30PM - 2:45PMMese, ChikakoGilman 381
AS.110.618 (01)Number TheoryMW 12:00PM - 1:15PMStaffShriver Hall 5
AS.110.633 (01)Harmonic AnalysisTTh 10:30AM - 11:45AMLindblad, HansShaffer 303
AS.110.726 (01)Topics in AnalysisTTh 12:00PM - 1:15PMSun, LimingGilman 10
AS.110.733 (01)Topics In Alg Num TheoryTTh 12:00PM - 1:15PMSavitt, David LawrenceSmokler Center Library
AS.110.801 (01)Thesis ResearchRiehl, Emily 
AS.110.801 (11)Thesis ResearchSavitt, David Lawrence 
AS.110.798 (01)Seminar in Number TheoryT 3:00PM - 4:30PMSmithling, Brian, Specter, Joel BenjaminHodson 316
AS.110.794 (01)Seminar in Category TheoryT 4:00PM - 6:30PMStaffGilman 377
AS.110.799 (01)Seminar in Algebraic GeometryT 4:00PM - 5:20PMZheng, XudongHodson 305
AS.110.791 (01)Seminar in Analysis and Partial Differential EquationsM 3:00PM - 5:20PMBernstein, JacobHodson 203
AS.110.757 (01)Topics in Stochastic Dynamical SystemsTTh 9:00AM - 10:15AMLu, FeiGarland 97
AS.110.790 (01)Seminar in Complex GeometryT 4:30PM - 5:45PMXu, HangGilman 17
AS.110.741 (01)Topics:Partial Differential EquationsMW 3:00PM - 4:15PMLindblad, HansGilman 77
AS.110.795 (01)Data Science SeminarW 3:00PM - 4:00PMMaggioni, MauroShaffer 303
AS.110.793 (01)Seminar in TopologyM 3:00PM - 5:20PMZakharevich, ValentinBloomberg 168
AS.110.801 (05)Thesis ResearchSpruck, Joel 
AS.110.801 (04)Thesis ResearchSogge, Christopher 
AS.110.801 (06)Thesis ResearchMaggioni, Mauro 
AS.110.801 (07)Thesis ResearchKitchloo, Nitya 
AS.110.801 (09)Thesis ResearchSmithling, Brian 
AS.110.801 (10)Thesis ResearchBernstein, Jacob 
AS.110.801 (08)Thesis ResearchShokurov, Vyacheslav 
AS.110.801 (03)Thesis ResearchLindblad, Hans 
AS.110.801 (02)Thesis ResearchConsani, Caterina 
AS.110.801 (12)Thesis ResearchDodson, Benjamin 
AS.110.801 (14)Thesis ResearchWang, Yi 
AS.110.801 (13)Thesis ResearchSire, Yannick