Graduate level research on a topic chosen by the professor and student.

• Days/Times:
• Instructor: Sire, Yannick
• Room:  
• Status: Open
• Seats Available: 49/50
• PosTag(s): n/a

The first of a two semester algebra sequence to provide the student with the foundations for Number Theory, Algebraic Geometry, Representation Theory, and other areas. Topics include refined elements of group theory, commutative algebra, Noetherian rings, local rings, modules, and rudiments of category theory, homological algebra, field theory, Galois theory, and non-commutative algebras.

• Days/Times: TTh 1:30PM - 2:45PM
• Instructor: Khovanov, Mikhail
• Room: Krieger 300
• Status: Open
• Seats Available: 17/24
• PosTag(s): n/a

This course covers the theory of the Lebesgue theory of integration in d-dimensional Euclidean space, and offers a brief introduction to the theory of Hilbert spaces. Closely related topics in real variables, such as functions of bounded variation, the Riemann-Stieltjes integral, Fubini's theorem, Lp classes, and various results about differentiation are examined in detail. applications are basic facts about convolution operators and Fourier series, including results for the conjugate function and the Hardy-Littlewood maximal function.

• Days/Times: MW 3:00PM - 4:15PM
• Instructor: Zhao, Zihui
• Room: Hodson 203
• Status: Open
• Seats Available: 23/24
• PosTag(s): n/a

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).

• Days/Times: MW 3:00PM - 4:15PM
• Instructor: Gregoric, Rok
• Room: Krieger 307
• Status: Open
• Seats Available: 13/15
• PosTag(s): n/a

Singular homology theory, cohomology and products, category theory and homological algebra, Künneth and universal coefficient theorems, Poincaré and Alexander duality theorems, Lefschetz fixed-point theorem, covering spaces and fundamental groups. Prerequsites: the equivalent of one semester in both Abstract Algebra and Real Analysis (specifically, point set topology).

• Days/Times: MW 1:30PM - 2:45PM
• Instructor: Staff
• Room: Bloomberg 276
• Status: Open
• Seats Available: 18/20
• PosTag(s): n/a

Elements of advanced algebra and number theory. Possible topics for the year-long sequence include local and global fields, Galois cohomology, semisimple algebras, class field theory, elliptic curves, modular and automorphic forms, integral representations of L-functions, adelic geometry and function fields, fundamental notions in arithmetic geometry (including Arakelov and diophantine geometry).

• Days/Times: TTh 9:00AM - 10:15AM
• Instructor: Corato Zanarella, Murilo
• Room: Krieger 307
• Status: Open
• Seats Available: 14/15
• PosTag(s): n/a

This course is the first in the sequence about the general theory of PDEs. The beginning of the course will describe several important results of functional analysis which are instrumental for the study of PDEs: Hahn-Banach theorem, Uniform boundedness and closed graph theorems, reflexive spaces and weak topologies. The topics covered include: theory of Sobolev spaces. Harmonic functions and their properties. Weyl theorem. General Elliptic operators. Existence theory for elliptic boundary value problems. Lax-Milgram theorem. Dirichlet principle. Fine properties of solutions of elliptic equations such as maximum principles, Harnack principles, Sobolev and H\"older regularity.

• Days/Times: MW 12:00PM - 1:15PM
• Instructor: Marshall-Stevens, Kobe
• Room: Hodson 315
• Status: Open
• Seats Available: 17/24
• PosTag(s): n/a

This class will explore basic aspects of functional analysis, focusing mostly on normed vector spaces. This will include the Hahn-Banach and open mapping theorems, a discussion of strong and weak topologies, the theory of compact operators, and spaces of integrable functions and Sobolev spaces, with applications to the study of some partial differential equations. Prerequisite: Real Analysis

• Days/Times: MW 10:30AM - 11:45AM
• Instructor: Lindblad, Hans
• Room: Krieger 411
• Status: Open
• Seats Available: 7/24
• PosTag(s): n/a

Introduction to affine varieties and projective varieties. Hilbert's theorems about polynomials in several variables with their connections to geometry. Abstract algebraic varieties and projective geometry. Dimension of varieties and smooth varieties. Sheaf theory and some notions of cohomology. Applications of sheaves to geometry; e.g., theory of divisors, rudiments of scheme theory for the understanding of the Riemann-Roch theorem for curves and surfaces. Other topics may include Jacobian varieties, resolution of singularities, birational geometry on surfaces, schemes, connections with complex analytic geometry and topology. 

• Days/Times: TTh 12:00PM - 1:15PM
• Instructor: Consani, Caterina (Katia)
• Room: Maryland 104
• Status: Open
• Seats Available: 13/15
• PosTag(s): n/a

This course is a graduate-level introduction to foundational material in Riemannian Geometry. Riemannian manifolds, a smooth manifold equipped with a Riemannian metric. Topics include connections, geodesics, Jacobi fields, submanifold theory including the second fundamental form and Gauss equations, manifolds of constant curvature, comparison theorems, Morse index theorem, Hadamard theorem and Bonnet-Myers theorem.

• Days/Times: TTh 10:30AM - 11:45AM
• Instructor: Wang, Yi
• Room: Gilman 186
• Status: Open
• Seats Available: 12/20
• PosTag(s): n/a

Topics covered will vary from year to year and are at the discretion of the instructor.

• Days/Times: TTh 4:30PM - 5:45PM
• Instructor: Savitt, David Lawrence
• Room: Bloomberg 276
• Status: Open
• Seats Available: 13/15
• PosTag(s): n/a

This is an independent study course for students interested in a working with a professor on a specific topic.

• Days/Times:
• Instructor: Riehl, EMILY
• Room:  
• Status: Open
• Seats Available: 4/5
• PosTag(s): n/a

This is an independent study course for students interested in a working with a professor on a specific topic.

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

This is an independent study course for students interested in a working with a professor on a specific topic.

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

This is an independent study course for students interested in a working with a professor on a specific topic.

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

This is an independent study course for students interested in a working with a professor on a specific topic.

• Days/Times:
• Instructor: Gepner, David James
• Room:  
• Status: Open
• Seats Available: 5/5
• PosTag(s): n/a

This is an independent study course for students interested in a working with a professor on a specific topic.

• Days/Times:
• Instructor: Sire, Yannick
• Room:  
• Status: Open
• Seats Available: 4/5
• PosTag(s): n/a

This is an independent study course for students interested in a working with a professor on a specific topic.

• Days/Times:
• Instructor: Lu, Fei
• Room:  
• Status: Open
• Seats Available: 5/5
• PosTag(s): n/a

This is an independent study course for students interested in a working with a professor on a specific topic.

• Days/Times:
• Instructor: Savitt, David Lawrence
• Room:  
• Status: Open
• Seats Available: 3/5
• PosTag(s): n/a

This is an independent study course for students interested in a working with a professor on a specific topic.

• Days/Times:
• Instructor: Mese, CHIKAKO
• Room:  
• Status: Open
• Seats Available: 5/5
• PosTag(s): n/a

This is an independent study course for students interested in a working with a professor on a specific topic.

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

This is an independent study course for students interested in a working with a professor on a specific topic.

• Days/Times:
• Instructor: Consani, Caterina (Katia)
• Room:  
• Status: Open
• Seats Available: 5/5
• PosTag(s): n/a

This is an independent study course for students interested in a working with a professor on a specific topic.

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

This is an independent study course for students interested in a working with a professor on a specific topic.

• Days/Times:
• Instructor: Sakellaridis, Yiannis
• Room:  
• Status: Open
• Seats Available: 5/5
• PosTag(s): n/a

This is an independent study course for students interested in a working with a professor on a specific topic.

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

This is an independent study course for students interested in a working with a professor on a specific topic.

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

This is an independent study course for students interested in a working with a professor on a specific topic.

• Days/Times:
• Instructor: Sunohara, Matthew
• Room:  
• Status: Open
• Seats Available: 5/5
• PosTag(s): n/a

This is an independent study course for students interested in a working with a professor on a specific topic.

• Days/Times:
• Instructor: Zhuang, Ziquan
• Room:  
• Status: Approval Required
• Seats Available: 5/5
• PosTag(s): n/a

This is an independent study course for students working with their advisor toward the completion of their thesis.

• Days/Times:
• Instructor: Riehl, EMILY
• Room:  
• Status: Open
• Seats Available: 25/25
• PosTag(s): n/a

This is an independent study course for students working with their advisor toward the completion of their thesis.

• Days/Times:
• Instructor: Consani, Caterina (Katia)
• Room:  
• Status: Open
• Seats Available: 25/25
• PosTag(s): n/a

This is an independent study course for students working with their advisor toward the completion of their thesis.

• Days/Times:
• Instructor: Lindblad, Hans
• Room:  
• Status: Open
• Seats Available: 25/25
• PosTag(s): n/a

This is an independent study course for students working with their advisor toward the completion of their thesis.

• Days/Times:
• Instructor: Sogge, Christopher Donald
• Room:  
• Status: Open
• Seats Available: 25/25
• PosTag(s): n/a

This is an independent study course for students working with their advisor toward the completion of their thesis.

• Days/Times:
• Instructor: Sakellaridis, Yiannis
• Room:  
• Status: Open
• Seats Available: 25/25
• PosTag(s): n/a

This is an independent study course for students working with their advisor toward the completion of their thesis.

• Days/Times:
• Instructor: Maggioni, Mauro
• Room:  
• Status: Open
• Seats Available: 24/25
• PosTag(s): n/a

This is an independent study course for students working with their advisor toward the completion of their thesis.

• Days/Times:
• Instructor: Kitchloo, Nitya
• Room:  
• Status: Open
• Seats Available: 25/25
• PosTag(s): n/a

This is an independent study course for students working with their advisor toward the completion of their thesis.

• Days/Times:
• Instructor: Shokurov, Vyacheslav
• Room:  
• Status: Open
• Seats Available: 24/25
• PosTag(s): n/a

This is an independent study course for students working with their advisor toward the completion of their thesis.

• Days/Times:
• Instructor: Wang, Yi
• Room:  
• Status: Open
• Seats Available: 10/10
• PosTag(s): n/a

This is an independent study course for students working with their advisor toward the completion of their thesis.

• Days/Times:
• Instructor: Bernstein, Jacob
• Room:  
• Status: Open
• Seats Available: 4/5
• PosTag(s): n/a

This is an independent study course for students working with their advisor toward the completion of their thesis.

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

This is an independent study course for students working with their advisor toward the completion of their thesis.

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

This is an independent study course for students working with their advisor toward the completion of their thesis.

• Days/Times:
• Instructor: Sire, Yannick
• Room:  
• Status: Open
• Seats Available: 4/5
• PosTag(s): n/a

This is an independent study course for students working with their advisor toward the completion of their thesis.

• Days/Times:
• Instructor: Gepner, David James
• Room:  
• Status: Open
• Seats Available: 5/5
• PosTag(s): n/a

This is an independent study course for students working with their advisor toward the completion of their thesis.

• Days/Times:
• Instructor: Lu, Fei
• Room:  
• Status: Open
• Seats Available: 5/5
• PosTag(s): n/a

This is an independent study course for students working with their advisor toward the completion of their thesis.

• Days/Times:
• Instructor: Han, Jingjun
• Room:  
• Status: Open
• Seats Available: 5/5
• PosTag(s): n/a

This is an independent study course for students working with their advisor toward the completion of their thesis.

• Days/Times:
• Instructor: Mese, CHIKAKO
• Room:  
• Status: Open
• Seats Available: 4/5
• PosTag(s): n/a

Graduate level research on a topic chosen by the professor and student.

• Days/Times:
• Instructor: Sire, Yannick
• Room:  
• Status: Open
• Seats Available: 45/45
• PosTag(s): n/a