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
• Days/Times: TTh 10:30AM - 11:45AM
• Instructor: Wang, Yi
• Room: Shaffer 301
• Status: Open
• Seats Available: 8/15

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
• Days/Times: MW 10:30AM - 11:45AM
• Instructor: Kitchloo, Nitya
• Room: Krieger 204
• Status: Open
• Seats Available: 10/15

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
• Days/Times: MW 1:30PM - 2:45PM
• Instructor: Sire, Yannick
• Room: Krieger 208
• Status: Open
• Seats Available: 10/15

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
• Days/Times: MW 1:30PM - 2:45PM
• Instructor: Bernstein, Jacob
• Room: Gilman 381
• Status: Open
• Seats Available: 9/15

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
• Days/Times: MW 12:00PM - 1:15PM
• Instructor: Dodson, Benjamin
• Room: Maryland 202
• Status: Open
• Seats Available: 7/15

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
• Days/Times: MW 12:00PM - 1:15PM
• Instructor: Shokurov, Vyacheslav
• Room: Greenhouse 113
• Status: Open
• Seats Available: 6/15

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
• Days/Times: MW 3:00PM - 4:15PM
• Instructor: Lindblad, Hans
• Room:  
• Status: Open
• Seats Available: 8/12

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
• Days/Times: TTh 9:00AM - 10:15AM
• Instructor: Mramor, Alexander Everest
• Room: Krieger 204
• Status: Open
• Seats Available: 16/20

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
• Days/Times: TTh 10:30AM - 11:45AM
• Instructor: Han, Jingjun
• Room: Krieger 204
• Status: Open
• Seats Available: 7/10

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
• Days/Times: TTh 12:00PM - 1:15PM
• Instructor: Sakellaridis, Ioannis
• Room: Krieger 204
• Status: Open
• Seats Available: 8/15

Topics In Alg Num Theory
AS.110.733 (01)

• Credits: 0.00
• Level: Graduate
• Days/Times: MW 3:00PM - 4:15PM
• Instructor: Savitt, David Lawrence
• Room:  
• Status: Open
• Seats Available: 5/12

Thesis Research
AS.110.801 (06)

• Credits: 0.00
• Level: Graduate
• Days/Times:
• Instructor: Maggioni, Mauro
• Room:  
• Status: Open
• Seats Available: 3/5

Thesis Research
AS.110.801 (02)

• Credits: 0.00
• Level: Graduate
• Days/Times:
• Instructor: Consani, Caterina
• Room:  
• Status: Open
• Seats Available: 4/5

Nash-Moser iteration and Kolmogorov-Arnold-Moser (KAM) theory
AS.110.741 (01)

KAM theory is aiming at constructing invariant (under the flow of a dynamical system in finite or infinite dimensions) tori (as in invariant manifold) for Hamiltonian systems. I will start by reminders about symplectic geometry and topology. Then I will present an easy proof of the Siegel theorem in complex analysis using an easy version of the KAM scheme. Several lectures will be dedicated to “hard implicit function theorems” via Nash-Moser iterations in Frechet spaces. I will then state the KAM theorem in its original form and its modern variants and I will provide the three different proofs of Kolmogorov, Arnold and Moser in finite dimensions. Finally, I will explain the major difficulties in the case of Hamiltonian PDEs to adapt the previous proofs and will move on to some known results such as the ones of Kuksin, Poeschel, Bourgain and De La Llave and myself. I will probably explain in detail the results of Bourgain for nonlinear Schrodinger.

• Credits: 0.00
• Level: Graduate
• Days/Times: MW 12:00PM - 1:15PM
• Instructor: Sire, Yannick
• Room: Krieger 204
• Status: Open
• Seats Available: 10/12

Thesis Research
AS.110.801 (04)

• Credits: 0.00
• Level: Graduate
• Days/Times:
• Instructor: Sogge, Christopher
• Room:  
• Status: Open
• Seats Available: 4/5

Thesis Research
AS.110.801 (05)

• Credits: 0.00
• Level: Graduate
• Days/Times:
• Instructor: Sakellaridis, Ioannis
• Room:  
• Status: Open
• Seats Available: 5/5

Thesis Research
AS.110.801 (01)

• Credits: 0.00
• Level: Graduate
• Days/Times:
• Instructor: Riehl, Emily
• Room:  
• Status: Open
• Seats Available: 3/5

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
• Days/Times: TTh 10:30AM - 11:45AM
• Instructor: Lu, Fei
• Room: Shriver Hall 104
• Status: Open
• Seats Available: 3/12

Thesis Research
AS.110.801 (03)

• Credits: 0.00
• Level: Graduate
• Days/Times:
• Instructor: Lindblad, Hans
• Room:  
• Status: Open
• Seats Available: 3/5

Thesis Research
AS.110.801 (10)

• Credits: 0.00
• Level: Graduate
• Days/Times:
• Instructor: Bernstein, Jacob
• Room:  
• Status: Open
• Seats Available: 5/5

Thesis Research
AS.110.801 (09)

• Credits: 0.00
• Level: Graduate
• Days/Times:
• Instructor: Wang, Yi
• Room:  
• Status: Open
• Seats Available: 4/5

Thesis Research
AS.110.801 (08)

• Credits: 0.00
• Level: Graduate
• Days/Times:
• Instructor: Shokurov, Vyacheslav
• Room:  
• Status: Open
• Seats Available: 2/5

Thesis Research
AS.110.801 (12)

• Credits: 0.00
• Level: Graduate
• Days/Times:
• Instructor: Dodson, Benjamin
• Room:  
• Status: Open
• Seats Available: 5/5

Thesis Research
AS.110.801 (13)

• Credits: 0.00
• Level: Graduate
• Days/Times:
• Instructor: Sire, Yannick
• Room:  
• Status: Open
• Seats Available: 5/5

Independent Study-Graduates
AS.110.800 (01)

• Credits: 0.00
• Level: Graduate
• Days/Times:
• Instructor: Maggioni, Mauro
• Room:  
• Status: Approval Required
• Seats Available: 3/3

Thesis Research
AS.110.801 (07)

• Credits: 0.00
• Level: Graduate
• Days/Times:
• Instructor: Kitchloo, Nitya
• Room:  
• Status: Open
• Seats Available: 5/5

Thesis Research
AS.110.801 (11)

• Credits: 0.00
• Level: Graduate
• Days/Times:
• Instructor: Savitt, David Lawrence
• Room:  
• Status: Open
• Seats Available: 1/5