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.110.615 (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: 15/20

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: Levering Arellano
  • Status: Open
  • Seats Available: 10/20

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: Mergenthaler 111
  • Status: Open
  • Seats Available: 13/20

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: Maryland 201
  • Status: Open
  • Seats Available: 5/15

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: Shaffer 303
  • Status: Open
  • Seats Available: 13/20

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: 10/30

Topics in Mathematical Physics
AS.110.712 (01)

  • Credits: 0.00
  • Level: Graduate
  • Days/Times: MW 1:30PM - 2:45PM
  • Instructor: Lindblad, Hans
  • Room:  
  • Status: Open
  • Seats Available: 2/8

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: Shaffer 303
  • Status: Open
  • Seats Available: 18/20

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: 4.00
  • Level: Graduate
  • Days/Times: TTh 10:30AM - 11:45AM
  • Instructor: Consani, Caterina
  • Room:  
  • Status: Open
  • Seats Available: 16/20

Thesis Research
AS.110.801 (07)

  • Credits: 4.00
  • Level: Graduate
  • Days/Times:
  • Instructor: Kitchloo, Nitya
  • Room:  
  • Status: Open
  • Seats Available: 25/25

Thesis Research
AS.110.801 (01)

  • Credits: 4.00
  • Level: Graduate
  • Days/Times:
  • Instructor: Riehl, Emily
  • Room:  
  • Status: Open
  • Seats Available: 22/25

Thesis Research
AS.110.801 (10)

  • Credits: 4.00
  • Level: Graduate
  • Days/Times:
  • Instructor: Bernstein, Jacob
  • Room:  
  • Status: Open
  • Seats Available: 4/5

Independent Study-Graduates
AS.110.800 (01)

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

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: 3/8

Independent Study-Graduates
AS.110.800 (02)

  • Credits: 0.00
  • Level: Graduate
  • Days/Times:
  • Instructor: Mramor, Alexander Everest
  • Room:  
  • Status: Open
  • Seats Available: 4/5

Thesis Research
AS.110.801 (16)

  • Credits: 4.00
  • Level: Graduate
  • Days/Times:
  • Instructor: Han, Jingjun
  • Room:  
  • Status: Open
  • Seats Available: 4/5

Introduction to Curvature Flows
AS.110.745 (01)

  • Credits: 0.00
  • Level: Graduate
  • Days/Times: TTh 3:00PM - 4:15PM
  • Instructor: Mramor, Alexander Everest
  • Room:  
  • Status: Open
  • Seats Available: 1/8

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.

  • Credits: 4.00
  • Level: Graduate
  • Days/Times: TTh 9:00AM - 10:15AM
  • Instructor: Han, Jingjun
  • Room: Shaffer 303
  • Status: Open
  • Seats Available: 15/19

Thesis Research
AS.110.801 (13)

  • Credits: 4.00
  • Level: Graduate
  • Days/Times:
  • Instructor: Sire, Yannick
  • Room:  
  • Status: Open
  • Seats Available: 3/5

Thesis Research
AS.110.801 (02)

  • Credits: 4.00
  • Level: Graduate
  • Days/Times:
  • Instructor: Consani, Caterina
  • Room:  
  • Status: Open
  • Seats Available: 24/25

Thesis Research
AS.110.801 (11)

  • Credits: 4.00
  • Level: Graduate
  • Days/Times:
  • Instructor: Savitt, David Lawrence
  • Room:  
  • Status: Open
  • Seats Available: 1/5

Thesis Research
AS.110.801 (09)

  • Credits: 4.00
  • Level: Graduate
  • Days/Times:
  • Instructor: Wang, Yi
  • Room:  
  • Status: Open
  • Seats Available: 10/10

Thesis Research
AS.110.801 (08)

  • Credits: 4.00
  • Level: Graduate
  • Days/Times:
  • Instructor: Shokurov, Vyacheslav
  • Room:  
  • Status: Open
  • Seats Available: 24/25

Thesis Research
AS.110.801 (12)

  • Credits: 4.00
  • Level: Graduate
  • Days/Times:
  • Instructor: Dodson, Benjamin
  • Room:  
  • Status: Open
  • Seats Available: 5/5

Thesis Research
AS.110.801 (06)

  • Credits: 4.00
  • Level: Graduate
  • Days/Times:
  • Instructor: Maggioni, Mauro
  • Room:  
  • Status: Open
  • Seats Available: 24/25

Topics In Alg Num Theory
AS.110.733 (02)

  • Credits: 0.00
  • Level: Graduate
  • Days/Times: MW 3:00PM - 4:15PM
  • Instructor: Savitt, David Lawrence
  • Room:  
  • Status: Canceled
  • Seats Available: 20/20

Thesis Research
AS.110.801 (04)

  • Credits: 4.00
  • Level: Graduate
  • Days/Times:
  • Instructor: Sogge, Christopher
  • Room:  
  • Status: Open
  • Seats Available: 24/25

Thesis Research
AS.110.801 (03)

  • Credits: 4.00
  • Level: Graduate
  • Days/Times:
  • Instructor: Lindblad, Hans
  • Room:  
  • Status: Open
  • Seats Available: 21/25

Thesis Research
AS.110.801 (05)

  • Credits: 4.00
  • Level: Graduate
  • Days/Times:
  • Instructor: Sakellaridis, Ioannis
  • Room:  
  • Status: Open
  • Seats Available: 25/25

Thesis Research
AS.110.801 (15)

  • Credits: 4.00
  • Level: Graduate
  • Days/Times:
  • Instructor: Lu, Fei
  • Room:  
  • Status: Open
  • Seats Available: 3/5

Thesis Research
AS.110.801 (14)

  • Credits: 4.00
  • Level: Graduate
  • Days/Times:
  • Instructor: Smithling, Brian
  • Room:  
  • Status: Open
  • Seats Available: 5/5

Course # (Section) Title Day/Times Instructor Room Info
AS.110.615 (01)Algebraic TopologyMW 10:30AM - 11:45AMKitchloo, Nitya 
AS.110.645 (01)Riemannian GeometryTTh 10:30AM - 11:45AMBernstein, JacobLevering Arellano
AS.110.605 (01)Real VariablesMW 12:00PM - 1:15PMSogge, ChristopherMergenthaler 111
AS.110.608 (01)Riemann SurfacesMW 12:00PM - 1:15PMMese, ChikakoMaryland 201
AS.110.632 (01)Partial Differential Equations IITTh 1:30PM - 2:45PMDodson, BenjaminShaffer 303
AS.110.637 (01)Functional AnalysisMW 12:00PM - 1:15PMLindblad, Hans 
AS.110.712 (01)Topics in Mathematical PhysicsMW 1:30PM - 2:45PMLindblad, Hans 
AS.110.601 (01)AlgebraTTh 12:00PM - 1:15PMShokurov, VyacheslavShaffer 303
AS.110.617 (01)Number TheoryTTh 10:30AM - 11:45AMConsani, Caterina 
AS.110.801 (07)Thesis ResearchKitchloo, Nitya 
AS.110.801 (01)Thesis ResearchRiehl, Emily 
AS.110.801 (10)Thesis ResearchBernstein, Jacob 
AS.110.800 (01)Independent Study-GraduatesRiehl, Emily 
AS.110.733 (01)Topics In Alg Num TheoryMW 1:30PM - 2:45PMSavitt, David Lawrence 
AS.110.800 (02)Independent Study-GraduatesMramor, Alexander Everest 
AS.110.801 (16)Thesis ResearchHan, Jingjun 
AS.110.745 (01)Introduction to Curvature FlowsTTh 3:00PM - 4:15PMMramor, Alexander Everest 
AS.110.643 (01)Algebraic GeometryTTh 9:00AM - 10:15AMHan, JingjunShaffer 303
AS.110.801 (13)Thesis ResearchSire, Yannick 
AS.110.801 (02)Thesis ResearchConsani, Caterina 
AS.110.801 (11)Thesis ResearchSavitt, David Lawrence 
AS.110.801 (09)Thesis ResearchWang, Yi 
AS.110.801 (08)Thesis ResearchShokurov, Vyacheslav 
AS.110.801 (12)Thesis ResearchDodson, Benjamin 
AS.110.801 (06)Thesis ResearchMaggioni, Mauro 
AS.110.733 (02)Topics In Alg Num TheoryMW 3:00PM - 4:15PMSavitt, David Lawrence 
AS.110.801 (04)Thesis ResearchSogge, Christopher 
AS.110.801 (03)Thesis ResearchLindblad, Hans 
AS.110.801 (05)Thesis ResearchSakellaridis, Ioannis 
AS.110.801 (15)Thesis ResearchLu, Fei 
AS.110.801 (14)Thesis ResearchSmithling, Brian