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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

Website: http://www.math.cornell.edu
Email: gradinfo@math.cornell.edu
Phone: 607 254-8993

316 Malott Hall
Cornell University
Ithaca, NY  14853

Subject and Degrees

Concentrations by Subject

Mathematics

  • mathematics

Faculty

Marcelo Aguiar

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

Dan Mihai Barbasch

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

Yuri Berest

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

Louis Joseph Billera

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

David S. Bindel

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

Kenneth Stephen Brown

  • Campus: Ithaca
  • Concentrations: Mathematics: mathematics
  • Research Interests: algebra; topology; group theory

Xiaodong Cao

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

Stephen Urban Chase

  • Campus: Ithaca - (Graduate School Professor)
  • Concentrations: Mathematics: mathematics
  • Research Interests: homological algebra; algebraic number theory

Robert Connelly

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

Robert Lee Constable

  • Campus: Ithaca
  • Concentrations: Mathematics: mathematics

Damek Shea Davis

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

R. Keith Dennis

  • Campus: Ithaca
  • Concentrations: Mathematics: mathematics
  • Research Interests: commutative and noncommutative algebra; algebraic K-theory

Clifford J Earle

  • Campus: Ithaca - (Graduate School Professor)
  • Concentrations: Mathematics: mathematics
  • Research Interests: complex variables; Teichmuller spaces

Leonard Gross

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

John Mark Guckenheimer

  • Campus: Ithaca - (Graduate School Professor)
  • Concentrations: Mathematics: mathematics
  • Research Interests: dynamical systems

Joseph Yehuda Halpern

  • Campus: Ithaca
  • Concentrations: Mathematics: mathematics

Daniel S Halpern-Leistner

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

Allen E Hatcher

  • Campus: Ithaca - (Graduate School Professor)
  • Concentrations: Mathematics: mathematics
  • Research Interests: geometric topology

Timothy James Healey

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

David Wilson Henderson

  • Campus: Ithaca - (Graduate School Professor)
  • Concentrations: Mathematics: mathematics
  • Research Interests: geometry; mathematics education

Tara S. Holm Riley

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

John Hamal Hubbard

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

Jiunn Tzon Hwang

  • Campus: Ithaca - (Graduate School Professor)
  • Concentrations: Mathematics: mathematics
  • Research Interests: statistics; confidence set theory

Yulij S Iliashenko

  • Campus: Ithaca - (Graduate School Professor)
  • Concentrations: Mathematics: mathematics
  • Research Interests: dynamical systems

Peter Jack Kahn

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

Jon M Kleinberg

  • 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.

Robert D. Kleinberg

  • 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.

Allen Knutson

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

Dexter Campbell Kozen

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

Lionel Levine

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

Jason F Manning

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

Karola Meszaros

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

Justin T. Moore

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

F. Camil Muscalu

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

Anil Nerode

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

Michael Nussbaum

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

Irena Vassileva Peeva

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

Ravi Kumar Ramakrishna

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

Richard Herbert Rand

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

James Renegar

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

Timothy R. Riley

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

Laurent Pascal Saloff-Coste

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

Gennady Samorodnitsky

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

Shankar Sen

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

Richard A Shore

  • Campus: Ithaca
  • Concentrations: Mathematics: mathematics
  • Research Interests: mathematical logic; recursion theory; set theory

Reyer Sjamaar

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

Charles Krug Smart

  • Campus: Ithaca
  • Concentrations: Mathematics: mathematics
  • Research Interests: nonlinear partial differential equations and probability.

John D Smillie

  • Campus: Ithaca - (Graduate School Professor)
  • Concentrations: Mathematics: mathematics
  • Research Interests: dynamical systems

Slawomir Solecki

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

Philippe Sosoe

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

Birgit Else Marie Speh

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

Michael Eugene Stillman

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

Robert Stephen Strichartz

  • Campus: Ithaca
  • Concentrations: Mathematics: mathematics
  • Research Interests: harmonic analysis; partial differential equations

Steven H Strogatz

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

Edward B Swartz

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

Nicolas P Templier

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

Alex John Townsend

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

Alexander B. Vladimirsky

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

Karen L Vogtmann

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

Marten Wegkamp

  • 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

James Edward West

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

Inna I. Zakharevich

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

David Zywina

  • 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.