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.

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:  
  • Status: Open
  • Seats Available: 15/15
  • 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
  • Days/Times: TTh 10:30AM - 11:45AM
  • Instructor: Dodson, Benjamin
  • Room:  
  • Status: Open
  • Seats Available: 14/15
  • PosTag(s): n/a

Algebraic Topology II
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 12:00PM - 1:15PM
  • Instructor: Riehl, Emily
  • Room:  
  • Status: Open
  • Seats Available: 14/15
  • PosTag(s): n/a

Number Theory II
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 3:00PM - 4:15PM
  • Instructor: Sakellaridis, Ioannis
  • Room:  
  • 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
  • Days/Times: TTh 10:30AM - 11:45AM
  • Instructor: Mese, Chikako
  • Room:  
  • Status: Open
  • Seats Available: 12/15
  • 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
  • Days/Times: MW 12:00PM - 1:15PM
  • Instructor: Gavrus, Cristian D
  • Room:  
  • Status: Open
  • Seats Available: 13/15
  • 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
  • Days/Times: TTh 10:30AM - 11:45AM
  • Instructor: Sogge, Christopher
  • Room:  
  • Status: Open
  • Seats Available: 6/15
  • PosTag(s): n/a

Algebraic Geometry II
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:  
  • Status: Open
  • Seats Available: 15/15
  • PosTag(s): n/a

Riemannian Geometry II
AS.110.646 (01)

The goal of the course is to provide basic notions on the theory of smooth manifolds: Tangent and cotangent bundles, submanifold theory, Lie group actions, Tensor analysis, Differential forms and De Rham cohomology, Integration theory, Hodge theory and Bochner technique. Recommended Course Background: AS.110.645.

  • Credits: 0.00
  • Level: Graduate
  • Days/Times: MW 12:00PM - 1:15PM
  • Instructor: Sire, Yannick
  • Room:  
  • Status: Open
  • Seats Available: 14/15
  • PosTag(s): n/a

Topics in Geometric Analysis
AS.110.731 (01)

  • Credits: 0.00
  • Level: Graduate
  • Days/Times: MW 12:00PM - 1:15PM
  • Instructor: Bernstein, Jacob
  • Room:  
  • Status: Open
  • Seats Available: 14/15
  • PosTag(s): n/a

Topics In Alg Num Theory
AS.110.733 (01)

  • Credits: 0.00
  • Level: Graduate
  • Days/Times: MW 1:30PM - 2:45PM
  • Instructor: Savitt, David Lawrence
  • Room:  
  • Status: Open
  • Seats Available: 12/12
  • PosTag(s): n/a

Topics in Analytic Number Theory
AS.110.739 (01)

This course will be on functional analysis (applied to number theory) and Connes-Meyer's spectral interpretation of zeroes of Hecke L functions. Topics will include : adeles, ideles, bornologies, spectral theory, condensed/liquid modules à la Scholze-Clausen, Pontryagin duality and almost-periodic functions, Tate's thesis, Connes-Meyer's spectral interpretation. Relations with category theory, quantum mechanics, Bost-Connes systems and non-commutative geometry will be evoked. This course will be designed to be appealing for students from analysis or from algebra.

  • Credits: 0.00
  • Level: Graduate
  • Days/Times: MW 9:00AM - 10:15AM
  • Instructor: Sagnier, Aurelien
  • Room:  
  • Status: Open
  • Seats Available: 8/8
  • PosTag(s): n/a

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
  • PosTag(s): n/a

Thesis Research
AS.110.801 (01)

  • Credits: 0.00
  • Level: Graduate
  • Days/Times:
  • Instructor: Riehl, Emily
  • Room:  
  • Status: Open
  • Seats Available: 5/5
  • PosTag(s): n/a

Thesis Research
AS.110.801 (02)

  • Credits: 0.00
  • Level: Graduate
  • Days/Times:
  • Instructor: Consani, Caterina
  • Room:  
  • Status: Open
  • Seats Available: 3/5
  • PosTag(s): n/a

Thesis Research
AS.110.801 (03)

  • Credits: 0.00
  • Level: Graduate
  • Days/Times:
  • Instructor: Lindblad, Hans
  • Room:  
  • Status: Open
  • Seats Available: 4/5
  • PosTag(s): n/a

Thesis Research
AS.110.801 (04)

  • Credits: 0.00
  • Level: Graduate
  • Days/Times:
  • Instructor: Sogge, Christopher
  • Room:  
  • Status: Open
  • Seats Available: 5/5
  • PosTag(s): n/a

Thesis Research
AS.110.801 (05)

  • Credits: 0.00
  • Level: Graduate
  • Days/Times:
  • Instructor: Sakellaridis, Ioannis
  • Room:  
  • Status: Open
  • Seats Available: 5/5
  • PosTag(s): n/a

Thesis Research
AS.110.801 (06)

  • Credits: 0.00
  • Level: Graduate
  • Days/Times:
  • Instructor: Maggioni, Mauro
  • Room:  
  • Status: Open
  • Seats Available: 5/5
  • PosTag(s): n/a

Thesis Research
AS.110.801 (07)

  • Credits: 0.00
  • Level: Graduate
  • Days/Times:
  • Instructor: Kitchloo, Nitya
  • Room:  
  • Status: Open
  • Seats Available: 5/5
  • PosTag(s): n/a

Thesis Research
AS.110.801 (08)

  • Credits: 0.00
  • Level: Graduate
  • Days/Times:
  • Instructor: Shokurov, Vyacheslav
  • Room:  
  • Status: Open
  • Seats Available: 5/5
  • PosTag(s): n/a

Thesis Research
AS.110.801 (09)

  • Credits: 0.00
  • Level: Graduate
  • Days/Times:
  • Instructor: Wang, Yi
  • Room:  
  • Status: Open
  • Seats Available: 5/5
  • PosTag(s): n/a

Thesis Research
AS.110.801 (10)

  • Credits: 0.00
  • Level: Graduate
  • Days/Times:
  • Instructor: Bernstein, Jacob
  • Room:  
  • Status: Open
  • Seats Available: 5/5
  • PosTag(s): n/a

Thesis Research
AS.110.801 (11)

  • Credits: 0.00
  • Level: Graduate
  • Days/Times:
  • Instructor: Savitt, David Lawrence
  • Room:  
  • Status: Open
  • Seats Available: 5/5
  • PosTag(s): n/a

Thesis Research
AS.110.801 (12)

  • Credits: 0.00
  • Level: Graduate
  • Days/Times:
  • Instructor: Dodson, Benjamin
  • Room:  
  • Status: Open
  • Seats Available: 5/5
  • PosTag(s): n/a

Thesis Research
AS.110.801 (13)

  • Credits: 0.00
  • Level: Graduate
  • Days/Times:
  • Instructor: Sire, Yannick
  • Room:  
  • Status: Open
  • Seats Available: 5/5
  • PosTag(s): n/a

Thesis Research
AS.110.801 (14)

  • Credits: 0.00
  • Level: Graduate
  • Days/Times:
  • Instructor: Wang, Yi
  • Room:  
  • Status: Open
  • Seats Available: 5/5
  • PosTag(s): n/a

Course # (Section) Title Day/Times Instructor Room PosTag(s) Info
AS.110.602 (01)AlgebraMW 12:00PM - 1:15PMShokurov, Vyacheslav 
AS.110.607 (01)Complex VariablesTTh 10:30AM - 11:45AMDodson, Benjamin 
AS.110.616 (01)Algebraic Topology IIMW 12:00PM - 1:15PMRiehl, Emily 
AS.110.618 (01)Number Theory IITTh 3:00PM - 4:15PMSakellaridis, Ioannis 
AS.110.619 (01)Lie Groups and Lie AlgebrasTTh 10:30AM - 11:45AMMese, Chikako 
AS.110.631 (01)Partial Differential Equations IMW 12:00PM - 1:15PMGavrus, Cristian D 
AS.110.633 (01)Harmonic AnalysisTTh 10:30AM - 11:45AMSogge, Christopher 
AS.110.644 (01)Algebraic Geometry IITTh 10:30AM - 11:45AMHan, Jingjun 
AS.110.646 (01)Riemannian Geometry IIMW 12:00PM - 1:15PMSire, Yannick 
AS.110.731 (01)Topics in Geometric AnalysisMW 12:00PM - 1:15PMBernstein, Jacob 
AS.110.733 (01)Topics In Alg Num TheoryMW 1:30PM - 2:45PMSavitt, David Lawrence 
AS.110.739 (01)Topics in Analytic Number TheoryMW 9:00AM - 10:15AMSagnier, Aurelien 
AS.110.800 (01)Independent Study-GraduatesMaggioni, Mauro 
AS.110.801 (01)Thesis ResearchRiehl, Emily 
AS.110.801 (02)Thesis ResearchConsani, Caterina 
AS.110.801 (03)Thesis ResearchLindblad, Hans 
AS.110.801 (04)Thesis ResearchSogge, Christopher 
AS.110.801 (05)Thesis ResearchSakellaridis, Ioannis 
AS.110.801 (06)Thesis ResearchMaggioni, Mauro 
AS.110.801 (07)Thesis ResearchKitchloo, Nitya 
AS.110.801 (08)Thesis ResearchShokurov, Vyacheslav 
AS.110.801 (09)Thesis ResearchWang, Yi 
AS.110.801 (10)Thesis ResearchBernstein, Jacob 
AS.110.801 (11)Thesis ResearchSavitt, David Lawrence 
AS.110.801 (12)Thesis ResearchDodson, Benjamin 
AS.110.801 (13)Thesis ResearchSire, Yannick 
AS.110.801 (14)Thesis ResearchWang, Yi