Algebra provides the mathematical tools to find unknown quantities from related known ones, the famous quadratic equation being a familiar example. The subject interacts with all of mathematics as well as many applied fields. For instance, symmetries of pyramids or cubes, or indeed any object, can be viewed through the lens of algebra.

From Walter Feit’s pioneering work in finite group theory in the middle part of the 20th century to Moss Sweedler’s work on Hopf algebras to Ken Brown’s text, Cohomology of Groups, algebra has a long and strong history at Cornell.

The tradition continues, though research specialties have changed as has the discipline over the decades. Today the algebra group at Cornell includes experts in algebraic geometry, computational methods and commutative algebra, group theory, number theory, and representation theory. There are significant overlaps with combinatorics, probability, and topology.  

Faculty Members

Marcelo Aguiar Algebra, combinatorics, category theory
Yuri Berest Representation theory, noncommutative geometry, mathematical physics
Daniel Halpern-Leistner Algebraic geometry, homological algebra, mathematical physics, and representation theory
Martin Kassabov Combinatorial group theory
Allen Knutson Algebraic geometry and algebraic combinatorics
Jason Manning Geometric group theory, geometric topology
Karola Meszaros Algebraic and geometric combinatorics
Irena Peeva Commutative algebra
Ravi Ramakrishna Algebraic number theory
Timothy Riley Geometric group theory
Shankar Sen Algebraic number theory
Birgit E. Speh Lie groups, automorphic forms, representation theory
Michael E. Stillman Algebraic geometry, computational algebra
Edward Swartz Combinatorics, topology, geometry, and commutative algebra
Nicolas Templier Number theory, automorphic forms, and mathematical physics
David Zywina       Number theory, arithmetic geometry

Emeritus and Other Faculty

Louis Billera Geometric and algebraic combinatorics  
Kenneth S. Brown  Algebra, topology, group theory
Stephen U. Chase          Non-commutative algebra, homological algebra, Hopf algebras, group theory                                         
R. Keith Dennis Commutative and non-commutative algebra, algebraic K-theory, group theory, mathematical bibliography
Christian Gaetz Algebraic combinatorics
Nima Hoda Geometric group theory
Peter J. Kahn Algebra, number theory, algebraic and differential topology
Marie MacDonald Number Theory, commutative Algebra, combinatorial geometry, university mathematics education
Ritvik Ramkumar Algebraic geometry, commutative algebra
Moss E. Sweedler Algebra, algorithms
Karen Vogtmann Topology, geometric group theory

Activities and Resources

Related people

Image of Yuri Berest
Yuri Berest


Image of Louis Billera
Louis Billera

Professor Emeritus

Image of Kenneth Brown
Kenneth Brown

Professor Emeritus

Image of Stephen U. Chase
Stephen U. Chase

Professor Emeritus

Image of R. Keith Dennis
R. Keith Dennis

Professor Emeritus

Image of Peter J. Kahn
Peter J. Kahn

Professor Emeritus

Image of Allen Knutson
Allen Knutson


Image of Yun Liu
Yun Liu

Ph.D Candidate

Image of Jason Manning
Jason Manning


Image of Karola Mészáros
Karola Mészáros

Associate Professor

Image of Irena Peeva
Irena Peeva


Image of Ravi Ramakrishna
Ravi Ramakrishna

Professor, Stephen H. Weiss Presidential Fellow

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Timothy Riley


Image of Shankar Sen
Shankar Sen


Image of Birgit Speh
Birgit Speh

Distinguished Professor of Arts and Sciences in Mathematics

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Edward Swartz


Image of Moss E. Sweedler
Moss E. Sweedler

Professor Emeritus

Image of Karen Vogtmann, FRS
Karen Vogtmann, FRS

Goldwin Smith Professor Emerita of Mathematics Professor, University of Warwick

Image of David Zywina
David Zywina

Assistant Professor

All research areas

Algebra    Analysis    Applied Mathematics    Combinatorics and Discrete Geometry    Geometry    Logic    Probability and Statistics    Topology