## Mathematics

### Field Description

The graduate program in the field of mathematics at Cornell leads to the Ph.D. degree, which takes most students five to 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. In addition to the usual areas of algebra, analysis and geometry, the department has outstanding groups in the areas of algebraic geometry, combinatorics, dynamical systems, logic, Lie groups, and partial differential equations, including their numerical treatment. The field also maintains close ties with distinguished graduate programs in the fields of applied mathematics, computer science, operations research, and statistics.

The field of mathematics requires that you pass a test of basic mathematical reading ability in one language other than English. The allowed languages are French, German, Russian, Chinese, Japanese, Spanish, and Portuguese, regardless of whether any of these is your native tongue. However, to ensure maximal relevance to your research area, your choice of language must be approved by your thesis advisor (special committee chair); if he/she has no opinion you may make your own choice.

Candidates must have some teaching experience prior to graduation, a one-semester appointment as a teaching assistant is the department minimum requirement.

Students seeking a minor in mathematics should contact the Director of Graduate Studies. A course work master's degree in computer science is available to students in the Ph.D. program in mathematics. Details are available from the graduate field office.**Application:**

Applicants must have completed the work for an undergraduate degree in mathematics. That work should have included a rigorous course in advanced calculus and real variable theory that will serve as an introduction to measure theory. The student should also have some familiarity with applications of advanced calculus and should have had courses in linear algebra and modern abstract algebra at an advanced level. Applicants are required to submit GRE general and mathematics subject test scores; scores need to be reported by January 4. Non-native English speaking applicants must also submit minimum TOEFL scores of Writing: 20, Listening: 15, Reading: 20, and Speaking: 22 (Internet-based test).

### Contact Information

Email: gradinfo@math.cornell.edu

Phone: 607 254-8993

316 Malott Hall

Cornell University

Ithaca, NY 14853

### Subject and Degrees

**Mathematics (Ph.D.)***(Ithaca)*

### Concentrations by Subject

#### Mathematics

- mathematics

### Faculty

**Concentrations:**

*Mathematics:*mathematics

**Research Interests:**Algebra, Combinatorics, Category Theory

**Concentrations:**

*Mathematics:*mathematics

**Research Interests:**representation theory of reductive Lie groups

**Concentrations:**

*Mathematics:*mathematics

**Research Interests:**PDE; algebra; mathematical physics

**Concentrations:**

*Mathematics:*mathematics

**Research Interests:**geometric and algebraic combinatorics

**Concentrations:**

*Mathematics:*mathematics

**Research Interests:**applied numerical linear algebra and scientific computing

**Concentrations:**

*Mathematics:*mathematics

**Research Interests:**algebra; topology; group theory

**Concentrations:**

*Mathematics:*mathematics

**Research Interests:**differential geometry; geometric analysis; nonlinear parabolic equations

**Concentrations:**

*Mathematics:*mathematics

**Research Interests:**homological algebra; algebraic number theory

**Concentrations:**

*Mathematics:*mathematics

**Research Interests:**geometry; rigidity; topology

**Concentrations:**

*Mathematics:*mathematics

**Concentrations:**

*Mathematics:*mathematics

**Research Interests:**continuous optimization and variational analysis

**Concentrations:**

*Mathematics:*mathematics

**Research Interests:**commutative and noncommutative algebra; algebraic K-theory

**Concentrations:**

*Mathematics:*mathematics

**Research Interests:**complex variables; Teichmuller spaces

**Concentrations:**

*Mathematics:*mathematics

**Research Interests:**functional analysis; analysis of path spaces

**Concentrations:**

*Mathematics:*mathematics

**Research Interests:**dynamical systems

**Concentrations:**

*Mathematics:*mathematics

**Concentrations:**

*Mathematics:*mathematics

**Research Interests:**moduli problems; geometric representation theory, derived algorithm geometry; derived categories of coherent sheaves

**Concentrations:**

*Mathematics:*mathematics

**Research Interests:**geometric topology

**Concentrations:**

*Mathematics:*mathematics

**Research Interests:**elliptic partial differential equations; nonlinear elasticity and analysis

**Concentrations:**

*Mathematics:*mathematics

**Research Interests:**symplectic geometry; algebraic topology; algabraic geometry

**Concentrations:**

*Mathematics:*mathematics

**Research Interests:**analysis; differential equations; differential geometry

**Concentrations:**

*Mathematics:*mathematics

**Research Interests:**statistics; confidence set theory

**Concentrations:**

*Mathematics:*mathematics

**Research Interests:**dynamical systems

**Concentrations:**

*Mathematics:*mathematics

**Research Interests:**differential and algebraic topology

**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.

**Concentrations:**

*Mathematics:*mathematics

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

**Concentrations:**

*Mathematics:*mathematics

**Research Interests:**algebraic geometry and algebraic combinations

**Concentrations:**

*Mathematics:*mathematics

**Research Interests:**computational theory; computational algebra and logic

**Concentrations:**

*Mathematics:*mathematics

**Research Interests:**Geometric group theory, geometric topology

**Concentrations:**

*Mathematics:*mathematics

**Research Interests:**Algebraic combinatorics and discrete geometry.

**Concentrations:**

*Mathematics:*mathematics

**Research Interests:**set theory; combinatorics; logic

**Concentrations:**

*Mathematics:*mathematics

**Research Interests:**mathematical logic; recursive functions, computer science

**Concentrations:**

*Mathematics:*mathematics

**Research Interests:**algebra

**Concentrations:**

*Mathematics:*mathematics

**Research Interests:**algebraic number theory

**Concentrations:**

*Mathematics:*mathematics

**Research Interests:**applied mathematics; differential equations

**Concentrations:**

*Mathematics:*mathematics

**Research Interests:**computational complexity; mathematical programming

**Concentrations:**

*Mathematics:*mathematics

**Research Interests:**geometric group theory

**Concentrations:**

*Mathematics:*mathematics

**Research Interests:**analysis and probability

**Concentrations:**

*Mathematics:*mathematics

**Research Interests:**algebraic number theory

**Concentrations:**

*Mathematics:*mathematics

**Research Interests:**mathematical logic; recursion theory; set theory

**Concentrations:**

*Mathematics:*mathematics

**Research Interests:**lie groups; differential geometry

**Concentrations:**

*Mathematics:*mathematics

**Research Interests:**nonlinear partial differential equations and probability.

**Concentrations:**

*Mathematics:*mathematics

**Research Interests:**dynamical systems

**Concentrations:**

*Mathematics:*mathematics

**Research Interests:**mathematical logic

**Concentrations:**

*Mathematics:*mathematics

**Research Interests:**probability, analysis, mathematical physics

**Concentrations:**

*Mathematics:*mathematics

**Research Interests:**Lie groups; automorphic forms

**Concentrations:**

*Mathematics:*mathematics

**Research Interests:**algebraic geometry; computational algebra

**Concentrations:**

*Mathematics:*mathematics

**Research Interests:**harmonic analysis; partial differential equations

**Concentrations:**

*Mathematics:*mathematics

**Research Interests:**nonlinear dynamics and chaos; coupled oscillators

**Concentrations:**

*Mathematics:*mathematics

**Research Interests:**combinatorics and discrete geometry

**Concentrations:**

*Mathematics:*mathematics

**Research Interests:**number theory, automorphic forms, arithmetic geometry, ergodic theory, quantum chaos.

**Concentrations:**

*Mathematics:*mathematics

**Research Interests:**numerical analysis and scientific computing

**Concentrations:**

*Mathematics:*mathematics

**Research Interests:**applied mathematics; numerical methods; dynamic systems; nonlinear PDEs; control theory

**Concentrations:**

*Mathematics:*mathematics

**Research Interests:**topology; geometric group theory

**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

**Concentrations:**

*Mathematics:*mathematics

**Research Interests:**geometric topology; infinite-dimensional topology

**Concentrations:**

*Mathematics:*mathematics

**Research Interests:**algebraic topology and algebraic K-theory

**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.