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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.  

 

Field Members

Marcelo Aguiar Algebra, combinatorics, category theory
Yuri Berest Representation theory, noncommutative geometry, mathematical physics
R. Keith Dennis Commutative and non-commutative algebra, algebraic K-theory, group theory, mathematical bibliography
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

Marie B.Langlois Number Theory, commutative Algebra, combinatorial geometry, university mathematics education
Julie Bergner Homotopy theory, algebraic topology
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                                         
Harrison Chen Derived algebraic geometry, representation theory
Benjamin Harris Abstract Harmonic Analysis
Brian Hwang Number theory, representation theory, algebraic geometry
Peter J. Kahn Algebra, number theory, algebraic and differential topology
Moss E. Sweedler Algebra, algorithms
Karen Vogtmann Topology, geometric group theory