# Current Courses

- AS.110.607 - Complex Variables
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**Instructor:**Xu, Hang**Term:**Spring 2018**Meetings:**TTh 10:30AM - 11:45AM**Status:**Open**Level:**Graduate**Departments:**AS Mathematics - AS.110.631 - Partial Differential Equations I
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**Instructor:**Sire, Yannick**Term:**Spring 2018**Meetings:**MW 9:00AM - 10:15AM**Status:**Open**Level:**Graduate**Departments:**AS Mathematics - AS.110.633 - Harmonic Analysis
Fourier multipliers, oscillatory integrals, restriction theorems, Fourier integral operators, pseudodifferential operators, eigenfunctions. Undergrads need instructor's permission.

**Credits:**0.00**Instructor:**Sogge, Christopher**Term:**Spring 2018**Meetings:**MW 1:30PM - 2:45PM**Status:**Open**Level:**Graduate**Departments:**AS Mathematics - AS.110.644 - Algebraic Geometry
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**Instructor:**Shokurov, Vyacheslav**Term:**Spring 2018**Meetings:**MW 3:00PM - 4:15PM**Status:**Open**Level:**Graduate**Departments:**AS Mathematics - AS.110.722 - Topics in Homotopy Theory
The course will focus on recent developments in homotopy theory, such as Galois theory for E_n (n \geq 2) ring-spectra, and on connections with number theory; in particular, work of Bhatt, Hesselholt, Lurie, Scholze and others on topological Hochschild homology and its applications to geometry over the p-adic complex numbers.

**Credits:**0.00**Instructor:**Riehl, Emily**Term:**Spring 2018**Meetings:**M 1:00PM - 2:00PM**Status:**Canceled**Level:**Graduate**Departments:**AS Mathematics - AS.110.742 - Topics In Partial Differential Equations
In this course we will be discussing some dispersive evolution equations, primarily the nonlinear Schrodinger equation. Topics will include well - posedness theory, conservation laws, and scattering. The course will be accessible to students who have not taken graduate partial differential equations or functional analysis.

**Credits:**0.00**Instructor:**Dodson, Benjamin**Term:**Spring 2018**Meetings:**MW 12:00PM - 1:15PM**Status:**Open**Level:**Graduate**Departments:**AS Mathematics - AS.110.790 - Seminar in Complex Geometry
Presentations of current research papers by faculty, graduate students and invited guest speakers. For graduate students only.

**Credits:**0.00**Instructor:**Shiffman, Bernard**Term:**Spring 2018**Meetings:**T 4:30PM - 5:45PM**Status:**Open**Level:**Graduate**Departments:**AS Mathematics - AS.110.712 - Topics in Mathematical Physics
**Credits:**0.00**Instructor:**Lindblad, Hans**Term:**Spring 2018**Meetings:**MW 3:00PM - 4:00PM**Status:**Open**Level:**Graduate**Departments:**AS Mathematics - AS.110.616 - Algebraic Topology
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**Instructor:**Riehl, Emily**Term:**Spring 2018**Meetings:**MW 1:30PM - 2:45PM**Status:**Open**Level:**Graduate**Departments:**AS Mathematics - AS.110.602 - Algebra
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**Instructor:**Consani, Caterina**Term:**Spring 2018**Meetings:**MW 10:30AM - 11:45AM**Status:**Open**Level:**Graduate**Departments:**AS Mathematics - AS.110.791 - Seminar in Analysis and Partial Differential Equations
Presentations of current research papers by faculty, graduate students and invited guest speakers. For graduate students only.

**Credits:**0.00**Instructor:**Staff**Term:**Spring 2018**Meetings:**M 3:00PM - 5:20PM**Status:**Open**Level:**Graduate**Departments:**AS Mathematics - AS.110.793 - Seminar in Topology
For graduate students only. Presentations of current research papers by faculty, graduate students and invited guest speakers.

**Credits:**0.00**Instructor:**Staff**Term:**Spring 2018**Meetings:**M 3:00PM - 5:20PM**Status:**Open**Level:**Graduate**Departments:**AS Mathematics - AS.110.795 - Data Science Seminar
Presentations of current research papers by faculty, graduate students and invited guest speakers. For graduate students only.

**Credits:**0.00**Instructor:**Maggioni, Mauro**Term:**Spring 2018**Meetings:**W 3:00PM - 4:00PM**Status:**Open**Level:**Graduate**Departments:**AS MathematicsEN Applied Mathematics & Statistics - AS.110.799 - Seminar in Algebraic Geometry
For graduate students only. Presentations of current research papers by faculty, graduate students and invited guest speakers.

**Credits:**4.00**Instructor:**Staff**Term:**Spring 2018**Meetings:**T 4:00PM - 5:20PM**Status:**Open**Level:**Graduate**Departments:**AS Mathematics - AS.110.801 - Thesis Research
**Credits:**0.00**Instructor:**Consani, Caterina**Term:**Spring 2018**Meetings:****Status:**Open**Level:**Graduate**Departments:**AS Mathematics - AS.110.801 - Thesis Research
**Credits:**0.00**Instructor:**Riehl, Emily**Term:**Spring 2018**Meetings:****Status:**Open**Level:**Graduate**Departments:**AS Mathematics - AS.110.798 - Seminar in Number Theory
**Credits:**0.00**Instructor:**Staff**Term:**Spring 2018**Meetings:**Th 3:00PM - 4:30PM**Status:**Open**Level:**Graduate**Departments:**AS Mathematics - AS.110.801 - Thesis Research
**Credits:**0.00**Instructor:**Maggioni, Mauro**Term:**Spring 2018**Meetings:****Status:**Open**Level:**Graduate**Departments:**AS Mathematics - AS.110.801 - Thesis Research
**Credits:**0.00**Instructor:**Savitt, David Lawrence**Term:**Spring 2018**Meetings:****Status:**Open**Level:**Graduate**Departments:**AS Mathematics - AS.110.801 - Thesis Research
**Credits:**0.00**Instructor:**Dodson, Benjamin**Term:**Spring 2018**Meetings:****Status:**Open**Level:**Graduate**Departments:**AS Mathematics - AS.110.801 - Thesis Research
**Credits:**0.00**Instructor:**Morava, Jack**Term:**Spring 2018**Meetings:****Status:**Open**Level:**Graduate**Departments:**AS Mathematics - AS.110.802 - Independent Student – Graduate
Statistical Learning and Estimation

**Credits:**0.00**Instructor:**Maggioni, Mauro**Term:**Spring 2018**Meetings:**M 1:00PM - 2:00PM**Status:**Canceled**Level:**Graduate**Departments:**AS Mathematics