Plimpton 322, a Babylonian table made about 3800 years ago that contains numerous triples $(a,b,c)$ satisfying $a^2+b^2=c^2$, including (119, 120, 169) and (4961, 6480, 8161). This predates Pythagoras by over 1000 years.

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.

Field Members

Algebra, combinatorics, category theory
Representation theory, noncommutative geometry, mathematical physics
Geometric and algebraic combinatorics
Commutative and non-commutative algebra, algebraic K-theory, group theory, mathematical bibliography
Algebraic geometry, homological algebra, mathematical physics, and representation theory
Combinatorial group theory
Algebraic geometry and algebraic combinatorics
Geometric group theory, geometric topology
Algebraic and geometric combinatorics
Commutative algebra
Algebraic number theory
Geometric group theory
Algebraic number theory
Lie groups, automorphic forms, representation theory
Algebraic geometry, computational algebra
Combinatorics, topology, geometry, and commutative algebra
Number theory, automorphic forms, and mathematical physics
Number theory, arithmetic geometry

Emeritus and Other Faculty

Algebra, topology, group theory
Non-commutative algebra, homological algebra, Hopf algebras, group theory
Representation theory of p-adic groups, and motivic integration
Number theory, representation theory, algebraic geometry
Algebra, number theory, algebraic and differential topology
Algebra, representation theory, and Lie groups
Combinatorics, algebraic geometry, commutative algebra
Algebra, algorithms
Topology, geometric group theory
Representation theory of reductive Lie groups

Activities and Resources