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 MacDonald | Number Theory, commutative Algebra, combinatorial geometry, university mathematics education | |

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 | |

James Hyde | Geometric group theory | |

Peter J. Kahn | Algebra, number theory, algebraic and differential topology | |

Moss E. Sweedler | Algebra, algorithms | |

Karen Vogtmann | Topology, geometric group theory |