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

Days/Times:

Instructor: Sire, Yannick

Room:

Status: Open

Seats Available: 14/50

PosTag(s): n/a

×

Algebra I AS.110.601 (01)

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: Gepner, David James

Room: Maryland 202

Status: Open

Seats Available: 11/24

PosTag(s): n/a

×

Real Variables AS.110.605 (01)

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: Sogge, Christopher Donald

Room: Maryland 202

Status: Open

Seats Available: 12/24

PosTag(s): n/a

×

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).

Days/Times: MW 12:00PM - 1:15PM

Instructor: Im, Mee Seong

Room: Bloomberg 178

Status: Open

Seats Available: 11/15

PosTag(s): n/a

×

Algebraic Topology I AS.110.615 (01)

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: Kitchloo, Nitya

Room: Maryland 104

Status: Open

Seats Available: 5/20

PosTag(s): n/a

×

Number Theory I AS.110.617 (01)

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: 6/15

PosTag(s): n/a

×

Partial Differential Equations I AS.110.631 (01)

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: Dodson, Benjamin

Room: Hodson 211

Status: Open

Seats Available: 18/24

PosTag(s): n/a

×

Functional Analysis AS.110.637 (01)

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 1:30PM - 2:45PM

Instructor: Park, Chamsol

Room: Maryland 202

Status: Open

Seats Available: 7/24

PosTag(s): n/a

×

Algebraic Geometry I AS.110.643 (01)

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: Shokurov, Vyacheslav

Room: Maryland 104

Status: Open

Seats Available: 8/15

PosTag(s): n/a

×

Riemannian Geometry I AS.110.645 (01)

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: Restrepo Montoya, Daniel Eduardo

Room: Maryland 202

Status: Open

Seats Available: 10/25

PosTag(s): n/a

×

Topics In Alg Num Theory AS.110.733 (01)

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: Maryland 217

Status: Open

Seats Available: 10/15

PosTag(s): n/a

×

Independent Study-Graduates AS.110.800 (01)

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

×

Independent Study-Graduates AS.110.800 (02)

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

×

Independent Study-Graduates AS.110.800 (03)

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

×

Independent Study-Graduates AS.110.800 (04)

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

×

Independent Study-Graduates AS.110.800 (05)

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: 3/5

PosTag(s): n/a

×

Independent Study-Graduates AS.110.800 (06)

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: 3/5

PosTag(s): n/a

×

Independent Study-Graduates AS.110.800 (07)

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

×

Independent Study-Graduates AS.110.800 (08)

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: 2/5

PosTag(s): n/a

×

Independent Study-Graduates AS.110.800 (09)

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

×

Independent Study-Graduates AS.110.800 (10)

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

×

Independent Study-Graduates AS.110.800 (11)

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

×

Independent Study-Graduates AS.110.800 (12)

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

×

Independent Study-Graduates AS.110.800 (13)

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

×

Independent Study-Graduates AS.110.800 (14)

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

×

Independent Study-Graduates AS.110.800 (15)

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

×

Independent Study-Graduates AS.110.800 (16)

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

Days/Times:

Instructor: Sunohara, Matthew Tyler Toyoharu

Room:

Status: Open

Seats Available: 4/5

PosTag(s): n/a

×

Thesis Research AS.110.801 (01)

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: 22/25

PosTag(s): n/a

×

Thesis Research AS.110.801 (02)

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: 24/25

PosTag(s): n/a

×

Thesis Research AS.110.801 (03)

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: 24/25

PosTag(s): n/a

×

Thesis Research AS.110.801 (04)

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: 22/25

PosTag(s): n/a

×

Thesis Research AS.110.801 (05)

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: 23/25

PosTag(s): n/a

×

Thesis Research AS.110.801 (06)

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

×

Thesis Research AS.110.801 (07)

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: 24/25

PosTag(s): n/a

×

Thesis Research AS.110.801 (08)

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

×

Thesis Research AS.110.801 (09)

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

×

Thesis Research AS.110.801 (10)

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: 3/5

PosTag(s): n/a

×

Thesis Research AS.110.801 (11)

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

×

Thesis Research AS.110.801 (12)

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: 4/5

PosTag(s): n/a

×

Thesis Research AS.110.801 (13)

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

×

Thesis Research AS.110.801 (14)

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: 2/5

PosTag(s): n/a

×

Thesis Research AS.110.801 (15)

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: 4/5

PosTag(s): n/a

×

Thesis Research AS.110.801 (16)

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

×

Thesis Research AS.110.801 (17)

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 Student Research AS.110.895 (01)

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

Days/Times:

Instructor: Sire, Yannick

Room:

Status: Open

Seats Available: 37/45

PosTag(s): n/a

×

Algebra II 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

Days/Times: TTh 3:00PM - 4:15PM

Instructor: Shokurov, Vyacheslav

Room: Krieger 411

Status: Open

Seats Available: 18/18

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

Days/Times: TTh 10:30AM - 11:45AM

Instructor: Wang, Yi

Room: Krieger 411

Status: Open

Seats Available: 12/12

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.

Days/Times: MW 1:30PM - 2:45PM

Instructor: Kitchloo, Nitya

Room: Bloomberg 172

Status: Open

Seats Available: 15/15

PosTag(s): n/a

×

Number Theory II AS.110.618 (01)

Topics in 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: Sakellaridis, Yiannis

Room: Bloomberg 178

Status: Open

Seats Available: 15/15

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.

Days/Times: TTh 12:00PM - 1:15PM

Instructor: Li, Huajie

Room: Greenhouse 113

Status: Open

Seats Available: 10/10

PosTag(s): n/a

×

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.

Days/Times: MW 1:30PM - 2:45PM

Instructor: Dodson, Benjamin

Room: Bloomberg 178

Status: Open

Seats Available: 12/12

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.

Days/Times: MW 12:00PM - 1:15PM

Instructor: Park, Chamsol

Room: Bloomberg 178

Status: Open

Seats Available: 15/15

PosTag(s): n/a

×

Algebraic Geometry II AS.110.644 (01)

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: Zhuang, Ziquan

Room: Krieger 411

Status: Open

Seats Available: 10/10

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.

Days/Times: MW 12:00PM - 1:15PM

Instructor: Restrepo Montoya, Daniel Eduardo

Room: Krieger 411

Status: Open

Seats Available: 15/15

PosTag(s): n/a

×

Stochastic Differential Equations: An Introduction With Applications AS.110.653 (01)

This course is an introduction to stochastic differential equations and applications. Basic topics to be reviewed include Ito and Stratonovich integrals, Ito formula, SDEs and their integration. The course will focus on diffusion processes and diffusion theory, with topics include Markov properties, generator, Kolmogrov’s equations (Fokker-Planck equation), Feynman-Kac formula, the martingale problem, Girsanov theorem, stability and ergodicity. The course will briefly introduce applications, with topics include statistical inference of SDEs, filtering and control.

Days/Times: MW 8:30AM - 9:45AM

Instructor: Wang, Xiong

Room: Krieger 411

Status: Open

Seats Available: 10/10

PosTag(s): n/a

×

Topics in Algebraic Geometry AS.110.737 (01)

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

Days/Times: TTh 12:00PM - 1:15PM

Instructor: Consani, Caterina (Katia)

Room: Hodson 313

Status: Open

Seats Available: 8/8

PosTag(s): n/a

×

Topics in Differential Geometry AS.110.749 (01)

In this class, we will study Aaron Naber and Jeff Cheeger's recent result on proving codimension four conjecture. We plan to talk about some early results of the structure on manifolds with lower Ricci bound by Cheeger and Colding. We will prove quantitative splitting theorem, volume convergence theorem, and the result that almost volume cone implies almost metric cone. Then we will discuss regularity of Einstein manifolds and the codimension four conjecture.

Days/Times:

Instructor: Staff

Room:

Status: Open

Seats Available: 10/10

PosTag(s): n/a

×

Mathematics GTA Teaching Seminar AS.110.771 (01)

The goals of this seminar center on the preparedness for graduate students in mathematics to engage in classroom instructions for undergraduates at Johns Hopkins University. This seminar augments the teaching orientation provided to graduate students by the CER and Mathematics Department by addressing (1) teaching-techniques: student-centered inclusive teaching strategies, facilitating small group work, incorporating student ideas and student thinking into active hole class discussions, and choosing appropriate mathematical tasks, (2) opportunities for practice teaching in classrooms before their first assignment to TA for a course in scaffolded micro-teaching experiences and (3) preparing for the practice of and documentation of a reflective teaching practice necessary for success in their careers as mathematicians and educators.

Days/Times: TTh 9:00AM - 10:15AM

Instructor: Braley, Emily

Room: Krieger 411

Status: Open

Seats Available: 15/15

PosTag(s): n/a

×

Independent Study-Graduates AS.110.800 (01)

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

Days/Times:

Instructor: Maggioni, Mauro

Room:

Status: Approval Required

Seats Available: 3/3

PosTag(s): n/a

×

Independent Study-Graduates AS.110.800 (02)

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: Approval Required

Seats Available: 5/5

PosTag(s): n/a

×

Independent Study-Graduates AS.110.800 (03)

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: Approval Required

Seats Available: 5/5

PosTag(s): n/a

×

Independent Study-Graduates AS.110.800 (06)

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: Approval Required

Seats Available: 5/5

PosTag(s): n/a

×

Independent Study-Graduates AS.110.800 (08)

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: Approval Required

Seats Available: 5/5

PosTag(s): n/a

×

Independent Study-Graduates AS.110.800 (15)

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: Approval Required

Seats Available: 5/5

PosTag(s): n/a

×

Independent Study-Graduates AS.110.800 (17)

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: Approval Required

Seats Available: 5/5

PosTag(s): n/a

×

Thesis Research AS.110.801 (01)

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: 5/5

PosTag(s): n/a

×

Thesis Research AS.110.801 (02)

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: 5/5

PosTag(s): n/a

×

Thesis Research AS.110.801 (03)

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: 5/5

PosTag(s): n/a

×

Thesis Research AS.110.801 (04)

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: 5/5

PosTag(s): n/a

×

Thesis Research AS.110.801 (05)

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: 5/5

PosTag(s): n/a

×

Thesis Research AS.110.801 (06)

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: 5/5

PosTag(s): n/a

×

Thesis Research AS.110.801 (07)

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: 5/5

PosTag(s): n/a

×

Thesis Research AS.110.801 (08)

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: 5/5

PosTag(s): n/a

×

Thesis Research AS.110.801 (09)

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: 5/5

PosTag(s): n/a

×

Thesis Research AS.110.801 (10)

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: 5/5

PosTag(s): n/a

Course # (Section)

Title

Day/Times

Instructor

Location

Term

Course Details

AS.110.802 (01)

Graduate Student Research

Sire, Yannick

Summer 2024

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

AS.110.601 (01)

Algebra I

TTh 1:30PM - 2:45PM

Gepner, David James

Maryland 202

Fall 2024

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.

AS.110.605 (01)

Real Variables

MW 3:00PM - 4:15PM

Sogge, Christopher Donald

Maryland 202

Fall 2024

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.

AS.110.608 (01)

Riemann Surfaces

MW 12:00PM - 1:15PM

Im, Mee Seong

Bloomberg 178

Fall 2024

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).

AS.110.615 (01)

Algebraic Topology I

MW 1:30PM - 2:45PM

Kitchloo, Nitya

Maryland 104

Fall 2024

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).

AS.110.617 (01)

Number Theory I

TTh 9:00AM - 10:15AM

Corato Zanarella, Murilo

Krieger 307

Fall 2024

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).

AS.110.631 (01)

Partial Differential Equations I

MW 12:00PM - 1:15PM

Dodson, Benjamin

Hodson 211

Fall 2024

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.

AS.110.637 (01)

Functional Analysis

MW 1:30PM - 2:45PM

Park, Chamsol

Maryland 202

Fall 2024

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

AS.110.643 (01)

Algebraic Geometry I

TTh 12:00PM - 1:15PM

Shokurov, Vyacheslav

Maryland 104

Fall 2024

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.

AS.110.645 (01)

Riemannian Geometry I

TTh 10:30AM - 11:45AM

Restrepo Montoya, Daniel Eduardo

Maryland 202

Fall 2024

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.

AS.110.733 (01)

Topics In Alg Num Theory

TTh 4:30PM - 5:45PM

Savitt, David Lawrence

Maryland 217

Fall 2024

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

AS.110.800 (01)

Independent Study-Graduates

Riehl, EMILY

Fall 2024

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

AS.110.800 (02)

Independent Study-Graduates

Bernstein, Jacob

Fall 2024

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

AS.110.800 (03)

Independent Study-Graduates

Kitchloo, Nitya

Fall 2024

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

AS.110.800 (04)

Independent Study-Graduates

Sogge, Christopher Donald

Fall 2024

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

AS.110.800 (05)

Independent Study-Graduates

Gepner, David James

Fall 2024

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

AS.110.800 (06)

Independent Study-Graduates

Sire, Yannick

Fall 2024

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

AS.110.800 (07)

Independent Study-Graduates

Lu, Fei

Fall 2024

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

AS.110.800 (08)

Independent Study-Graduates

Savitt, David Lawrence

Fall 2024

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

AS.110.800 (09)

Independent Study-Graduates

Mese, CHIKAKO

Fall 2024

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

AS.110.800 (10)

Independent Study-Graduates

Wang, Yi

Fall 2024

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

AS.110.800 (11)

Independent Study-Graduates

Consani, Caterina (Katia)

Fall 2024

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

AS.110.800 (12)

Independent Study-Graduates

Lindblad, Hans

Fall 2024

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

AS.110.800 (13)

Independent Study-Graduates

Sakellaridis, Yiannis

Fall 2024

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

AS.110.800 (14)

Independent Study-Graduates

Dodson, Benjamin

Fall 2024

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

AS.110.800 (15)

Independent Study-Graduates

Shokurov, Vyacheslav

Fall 2024

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

AS.110.800 (16)

Independent Study-Graduates

Sunohara, Matthew Tyler Toyoharu

Fall 2024

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

AS.110.801 (01)

Thesis Research

Riehl, EMILY

Fall 2024

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

AS.110.801 (02)

Thesis Research

Consani, Caterina (Katia)

Fall 2024

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

AS.110.801 (03)

Thesis Research

Lindblad, Hans

Fall 2024

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

AS.110.801 (04)

Thesis Research

Sogge, Christopher Donald

Fall 2024

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

AS.110.801 (05)

Thesis Research

Sakellaridis, Yiannis

Fall 2024

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

AS.110.801 (06)

Thesis Research

Maggioni, Mauro

Fall 2024

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

AS.110.801 (07)

Thesis Research

Kitchloo, Nitya

Fall 2024

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

AS.110.801 (08)

Thesis Research

Shokurov, Vyacheslav

Fall 2024

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

AS.110.801 (09)

Thesis Research

Wang, Yi

Fall 2024

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

AS.110.801 (10)

Thesis Research

Bernstein, Jacob

Fall 2024

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

AS.110.801 (11)

Thesis Research

Savitt, David Lawrence

Fall 2024

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

AS.110.801 (12)

Thesis Research

Dodson, Benjamin

Fall 2024

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

AS.110.801 (13)

Thesis Research

Sire, Yannick

Fall 2024

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

AS.110.801 (14)

Thesis Research

Gepner, David James

Fall 2024

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

AS.110.801 (15)

Thesis Research

Lu, Fei

Fall 2024

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

AS.110.801 (16)

Thesis Research

Han, Jingjun

Fall 2024

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

AS.110.801 (17)

Thesis Research

Mese, CHIKAKO

Fall 2024

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

AS.110.895 (01)

Graduate Student Research

Sire, Yannick

Fall 2024

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

AS.110.602 (01)

Algebra II

TTh 3:00PM - 4:15PM

Shokurov, Vyacheslav

Krieger 411

Spring 2025

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

AS.110.607 (01)

Complex Variables

TTh 10:30AM - 11:45AM

Wang, Yi

Krieger 411

Spring 2025

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

AS.110.616 (01)

Algebraic Topology II

MW 1:30PM - 2:45PM

Kitchloo, Nitya

Bloomberg 172

Spring 2025

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.

AS.110.618 (01)

Number Theory II

TTh 9:00AM - 10:15AM

Sakellaridis, Yiannis

Bloomberg 178

Spring 2025

Topics in 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).

AS.110.619 (01)

Lie Groups and Lie Algebras

TTh 12:00PM - 1:15PM

Li, Huajie

Greenhouse 113

Spring 2025

Lie groups and Lie algebras, classification of complex semi-simple Lie algebras, compact forms, representations and Weyl formulas, symmetric Riemannian spaces.

AS.110.632 (01)

Partial Differential Equations II

MW 1:30PM - 2:45PM

Dodson, Benjamin

Bloomberg 178

Spring 2025

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.

AS.110.633 (01)

Harmonic Analysis

MW 12:00PM - 1:15PM

Park, Chamsol

Bloomberg 178

Spring 2025

Fourier multipliers, oscillatory integrals, restriction theorems, Fourier integral operators, pseudodifferential operators, eigenfunctions. Undergrads need instructor's permission.

AS.110.644 (01)

Algebraic Geometry II

TTh 12:00PM - 1:15PM

Zhuang, Ziquan

Krieger 411

Spring 2025

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.

AS.110.646 (01)

Riemannian Geometry II

MW 12:00PM - 1:15PM

Restrepo Montoya, Daniel Eduardo

Krieger 411

Spring 2025

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.

AS.110.653 (01)

Stochastic Differential Equations: An Introduction With Applications

MW 8:30AM - 9:45AM

Wang, Xiong

Krieger 411

Spring 2025

This course is an introduction to stochastic differential equations and applications. Basic topics to be reviewed include Ito and Stratonovich integrals, Ito formula, SDEs and their integration. The course will focus on diffusion processes and diffusion theory, with topics include Markov properties, generator, Kolmogrov’s equations (Fokker-Planck equation), Feynman-Kac formula, the martingale problem, Girsanov theorem, stability and ergodicity. The course will briefly introduce applications, with topics include statistical inference of SDEs, filtering and control.

AS.110.737 (01)

Topics in Algebraic Geometry

TTh 12:00PM - 1:15PM

Consani, Caterina (Katia)

Hodson 313

Spring 2025

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

AS.110.749 (01)

Topics in Differential Geometry

Staff

Spring 2025

In this class, we will study Aaron Naber and Jeff Cheeger's recent result on proving codimension four conjecture. We plan to talk about some early results of the structure on manifolds with lower Ricci bound by Cheeger and Colding. We will prove quantitative splitting theorem, volume convergence theorem, and the result that almost volume cone implies almost metric cone. Then we will discuss regularity of Einstein manifolds and the codimension four conjecture.

AS.110.771 (01)

Mathematics GTA Teaching Seminar

TTh 9:00AM - 10:15AM

Braley, Emily

Krieger 411

Spring 2025

The goals of this seminar center on the preparedness for graduate students in mathematics to engage in classroom instructions for undergraduates at Johns Hopkins University. This seminar augments the teaching orientation provided to graduate students by the CER and Mathematics Department by addressing (1) teaching-techniques: student-centered inclusive teaching strategies, facilitating small group work, incorporating student ideas and student thinking into active hole class discussions, and choosing appropriate mathematical tasks, (2) opportunities for practice teaching in classrooms before their first assignment to TA for a course in scaffolded micro-teaching experiences and (3) preparing for the practice of and documentation of a reflective teaching practice necessary for success in their careers as mathematicians and educators.

AS.110.800 (01)

Independent Study-Graduates

Maggioni, Mauro

Spring 2025

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

AS.110.800 (02)

Independent Study-Graduates

Riehl, EMILY

Spring 2025

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

AS.110.800 (03)

Independent Study-Graduates

Kitchloo, Nitya

Spring 2025

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

AS.110.800 (06)

Independent Study-Graduates

Sire, Yannick

Spring 2025

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

AS.110.800 (08)

Independent Study-Graduates

Savitt, David Lawrence

Spring 2025

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

AS.110.800 (15)

Independent Study-Graduates

Shokurov, Vyacheslav

Spring 2025

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

AS.110.800 (17)

Independent Study-Graduates

Mese, CHIKAKO

Spring 2025

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

AS.110.801 (01)

Thesis Research

Riehl, EMILY

Spring 2025

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

AS.110.801 (02)

Thesis Research

Consani, Caterina (Katia)

Spring 2025

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

AS.110.801 (03)

Thesis Research

Lindblad, Hans

Spring 2025

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

AS.110.801 (04)

Thesis Research

Sogge, Christopher Donald

Spring 2025

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

AS.110.801 (05)

Thesis Research

Sakellaridis, Yiannis

Spring 2025

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

AS.110.801 (06)

Thesis Research

Maggioni, Mauro

Spring 2025

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

AS.110.801 (07)

Thesis Research

Kitchloo, Nitya

Spring 2025

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

AS.110.801 (08)

Thesis Research

Shokurov, Vyacheslav

Spring 2025

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

AS.110.801 (09)

Thesis Research

Wang, Yi

Spring 2025

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

AS.110.801 (10)

Thesis Research

Bernstein, Jacob

Spring 2025

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