The five main areas of concentration are Algebra, Analysis, Combinatorics, Geometry/Topology, and Statistics/Probability. Below are more specific research areas along with the names of faculty members most closely involved.

**Algebraic and Geometric Topology**

- Laura Anderson
- Robert Bieri
- Michael Dobbins
- Casey Donoven
- Ross Geoghegan
- Cary Malkiewich
- Pedro Ontaneda
- Russell Ricks
- Jonathan Williams

**Algebra related to logic and computer science**

**Arithmetic Algebraic Geometry**

**Geometry of Manifolds**

**Graph Theory**

**Group Theory**

- Robert Bieri
- Benjamin Brewster
- Matthew Brin
- Ross Geoghegan
- Fernando Guzman
- Marcin Mazur
- Hung Tong-Viet

**Number Theory**

**Partial Differential Equations**

**Probability**

**Representation Theory**

**Statistics**

**Statistical Machine Learning**