# Mathematics

## Field Description

The graduate program in the field of mathematics at Cornell leads to the Ph.D. degree, which takes most students six years of graduate study to complete. One feature that makes the program at Cornell particularly attractive is the broad range of interests of the faculty. The department has outstanding groups in the areas of algebra, algebraic geometry, analysis, applied mathematics, combinatorics, dynamical systems, geometry, logic, Lie groups, number theory, probability, and topology. The field also maintains close ties with distinguished graduate programs in the fields of applied mathematics, computer science, operations research, and statistics and data science.

**Application:**

Applicants must demonstrate mastery of the material required for an undergraduate major in mathematics. The mathematics field welcomes applications from and admits students with various mathematics backgrounds. GRE General and Subject Test scores are not required and will not be considered. Detailed academic requirements can be located in the graduate field handbook. Applicants must meet the minimum Graduate School Requirements, including the English Language Proficiency Requirement for all applicants

## Contact Information

Website: http://www.math.cornell.eduEmail: gradinfo@math.cornell.edu

Phone: 607 254-8993

316 Malott Hall

Cornell University

Ithaca, NY 14853

## Data and Statistics

## Field Manual

## Subject and Degrees

### Mathematics

## Concentrations by Subject

### Mathematics

- mathematics

## Faculty

**Campus:**Ithaca**Concentrations:***Mathematics:*mathematics**Research Interests:**Algebra, Combinatorics, Category Theory

**Campus:**Ithaca**Concentrations:***Mathematics:*mathematics**Research Interests:**representation theory of reductive Lie groups

**Campus:**Ithaca**Concentrations:***Mathematics:*mathematics**Research Interests:**PDE; algebra; mathematical physics

**Campus:**Ithaca - (Graduate School Professor)**Concentrations:***Mathematics:*mathematics**Research Interests:**geometric and algebraic combinatorics

**Campus:**Ithaca**Concentrations:***Mathematics:*mathematics**Research Interests:**applied numerical linear algebra and scientific computing

**Campus:**Ithaca - (Graduate School Professor)**Concentrations:***Mathematics:*mathematics**Research Interests:**algebra; topology; group theory

**Campus:**Ithaca**Concentrations:***Mathematics:*mathematics**Research Interests:**differential geometry; geometric analysis; nonlinear parabolic equations

**Campus:**Ithaca**Concentrations:***Mathematics:*mathematics**Research Interests:**geometry; rigidity; topology

**Campus:**Ithaca**Concentrations:***Mathematics:*mathematics**Research Interests:**Scientific Computing

**Campus:**Ithaca**Concentrations:***Mathematics:*mathematics**Research Interests:**continuous optimization and variational analysis

**Campus:**Ithaca - (Minor Member)**Concentrations:***Mathematics:*mathematics**Research Interests:**Geometry & Topology

**Campus:**Ithaca**Concentrations:***Mathematics:*mathematics**Research Interests:**Geometry, Dynamical systems, Riemann surfaces

**Campus:**Ithaca - (Graduate School Professor)**Concentrations:***Mathematics:*mathematics**Research Interests:**functional analysis; analysis of path spaces

**Campus:**Ithaca**Concentrations:***Mathematics:*mathematics

**Campus:**Ithaca**Concentrations:***Mathematics:*mathematics**Research Interests:**moduli problems; geometric representation theory, derived algorithm geometry; derived categories of coherent sheaves

**Campus:**Ithaca**Concentrations:***Mathematics:*mathematics**Research Interests:**elliptic partial differential equations; nonlinear elasticity and analysis

**Campus:**Ithaca**Concentrations:***Mathematics:*mathematics**Research Interests:**symplectic geometry; algebraic topology; algebraic geometry

**Campus:**Ithaca**Concentrations:***Mathematics:*mathematics**Research Interests:**analysis; differential equations; differential geometry

**Campus:**Ithaca - (Graduate School Professor)**Concentrations:***Mathematics:*mathematics**Research Interests:**differential and algebraic topology

**Campus:**Ithaca**Concentrations:***Mathematics:*mathematics**Research Interests:**topology; lie groups; representation theory; graph theory; geometric/combinatorical group theory

**Campus:**Ithaca**Concentrations:***Mathematics:*mathematics**Research Interests:**Issues at the interface of networks and information, with an emphasis on the social and information networks that underpin the Web and other on-line media.

**Campus:**Ithaca**Concentrations:***Mathematics:*mathematics**Research Interests:**Algorithms and theoretical computer science, especially economic aspects of algorithms, online learning and its applications, random processes in networks.

**Campus:**Ithaca**Concentrations:***Mathematics:*mathematics**Research Interests:**algebraic geometry and algebraic combinations

**Campus:**Ithaca**Concentrations:***Mathematics:*mathematics**Research Interests:**computational theory; computational algebra and logic

**Campus:**Ithaca**Concentrations:***Mathematics:*mathematics**Research Interests:**

**Campus:**Ithaca**Concentrations:***Mathematics:*mathematics

**Campus:**Ithaca**Concentrations:***Mathematics:*mathematics**Research Interests:**Dynamics and Geometry

**Campus:**Ithaca**Concentrations:***Mathematics:*mathematics**Research Interests:**Geometric Topology

**Campus:**Ithaca**Concentrations:***Mathematics:*mathematics**Research Interests:**Geometric group theory, geometric topology

**Campus:**Ithaca**Concentrations:***Mathematics:*mathematics**Research Interests:**Algebraic combinatorics and discrete geometry.

**Campus:**Ithaca**Concentrations:***Mathematics:*mathematics**Research Interests:**set theory; combinatorics; logic

**Campus:**Ithaca**Concentrations:***Mathematics:*mathematics**Research Interests:**mathematics

**Campus:**Ithaca**Concentrations:***Mathematics:*mathematics**Research Interests:**mathematical logic; recursive functions, computer science

**Campus:**Ithaca**Concentrations:***Mathematics:*mathematics**Research Interests:**statistics

**Campus:**Ithaca**Concentrations:***Mathematics:*mathematics**Research Interests:**algebra

**Campus:**Ithaca**Concentrations:***Mathematics:*mathematics**Research Interests:**Applied Probability

**Campus:**Ithaca**Concentrations:***Mathematics:*mathematics**Research Interests:**algebraic number theory

**Campus:**Ithaca**Concentrations:***Mathematics:*mathematics**Research Interests:**applied mathematics; differential equations

**Campus:**Ithaca**Concentrations:***Mathematics:*mathematics**Research Interests:**computational complexity; mathematical programming

**Campus:**Ithaca**Concentrations:***Mathematics:*mathematics**Research Interests:**geometric group theory

**Campus:**Ithaca**Concentrations:***Mathematics:*mathematics**Research Interests:**analysis and probability

**Campus:**Ithaca**Concentrations:***Mathematics:*mathematics**Research Interests:**

**Campus:**Ithaca**Concentrations:***Mathematics:*mathematics**Research Interests:**algebraic number theory

**Campus:**Ithaca**Concentrations:***Mathematics:*mathematics**Research Interests:**lie groups; differential geometry

**Campus:**Ithaca**Concentrations:***Mathematics:*mathematics**Research Interests:**mathematical logic

**Campus:**Ithaca**Concentrations:***Mathematics:*mathematics**Research Interests:**probability, analysis, mathematical physics

**Campus:**Ithaca**Concentrations:***Mathematics:*mathematics**Research Interests:**Lie groups; automorphic forms

**Campus:**Ithaca**Concentrations:***Mathematics:*mathematics**Research Interests:**Theory of Computation

**Campus:**Ithaca**Concentrations:***Mathematics:*mathematics**Research Interests:**Differential geometry

**Campus:**Ithaca**Concentrations:***Mathematics:*mathematics**Research Interests:**algebraic geometry; computational algebra

**Campus:**Ithaca**Concentrations:***Mathematics:*mathematics**Research Interests:**nonlinear dynamics and chaos; coupled oscillators

**Campus:**Ithaca**Concentrations:***Mathematics:*mathematics**Research Interests:**combinatorics and discrete geometry

**Campus:**Ithaca**Concentrations:***Mathematics:*mathematics**Research Interests:**Algorithm Design and Algorithmic Game Theory. Algorithmic game theory, an emerging new area of designing systems and algorithms for selfish users. My research focuses algorithms and games on graphs or networks. I am mostly interested in designing algorithms and games that provide provably close-to-optimal results.

**Campus:**Ithaca**Concentrations:***Mathematics:*mathematics**Research Interests:**number theory, automorphic forms, arithmetic geometry, ergodic theory, quantum chaos.

**Campus:**Ithaca**Concentrations:***Mathematics:*mathematics**Research Interests:**numerical analysis and scientific computing

**Campus:**Ithaca**Concentrations:***Mathematics:*mathematics**Research Interests:**applied mathematics; numerical methods; dynamic systems; nonlinear PDEs; control theory

**Campus:**Ithaca - (Minor Member)**Concentrations:***Mathematics:*mathematics**Research Interests:**Classification, Copula Modeling, Learning Theory, Empirical Process Theory, Machine Learning, Matrix Estimation and Completion, Model Selection and Aggregation, Nonparametric estimation

**Campus:**Ithaca**Concentrations:***Mathematics:*mathematics**Research Interests:**geometric topology; infinite-dimensional topology

**Campus:**Ithaca**Concentrations:***Mathematics:*mathematics**Research Interests:**Numerical Analysis, Inverse Problems, Optimal Transportation, Machine Learning, and Nonconvex Optimization

**Campus:**Ithaca**Concentrations:***Mathematics:*mathematics**Research Interests:**algebraic topology and algebraic K-theory

**Campus:**Ithaca**Concentrations:***Mathematics:*mathematics**Research Interests:**Geometric Analysis; Calculus of Variations; General Relativity

**Campus:**Ithaca**Concentrations:***Mathematics:*mathematics**Research Interests:**Number theory, arithmetic geometry My research is in number theory and more specifically in arithmetic geometry. I like to study the family of compatible Galois representations associated to various arithmetic objects (eg. abelian varieties, modular forms, Drinfeld modules); these representations encode much, if not all, of the arithmetic of the originally object. Galois representations can also be used to study the absolute the Galois group of the rational numbers, and I have recently been playing with some applications to the Inverse Galois Problem.