Algebra

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
Michael E. Stillman	Algebraic geometry, computational algebra
Edward Swartz	Combinatorics, topology, geometry, and commutative algebra
Nicolas Templier	Number theory, automorphic forms, and mathematical physics
Rachel Webb	Problems related to Gromov-Witten theory
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
Shiliang Gao	Algebraic combinatorics
Andreea Iorga	Algebraic number theory
Peter J. Kahn	Algebra, number theory, algebraic and differential topology
Marie MacDonald	Number Theory, commutative Algebra, combinatorial geometry, university mathematics education
Anton Mosunov	Number theory
Ritvik Ramkumar	Algebraic geometry, commutative algebra
Shankar Sen	Algebraic number theory
Birgit E. Speh	Lie groups, automorphic forms, representation theory
Moss E. Sweedler	Algebra, algorithms
Karen Vogtmann	Topology, geometric group theory