The Algebra Group at UB has various research interests in the areas of: Algebraic Number Theory; Arithmetic Geometry; Automorphic Forms; Categorical Algebra; Cryptography; L-functions; and, Representation Theory.

Our faculty have interests in multiple branches of mathematics relating to Analysis: Analytic Number Theory; Automorphic Forms; Complex Geometry; Dynamical Systems; Functional Analysis; Harmonic Analysis; Operator Algebras; Operator Theory; and, Quantum Field Theory.

The applied math group has particular strengths in nonlinear waves, network science and scientific computing, as well as breadth in a number of areas such as dynamical systems, mathematical finance and materials science / continuum mechanics. A number of our faculty participate in cross-disciplinary initiatives like the Institute for Artificial Intelligence and Data Science.

The geometry and topology group at UB is traditionally strong in research and mentoring. Our faculty work in the areas of algebraic topology, complex geometry, differential geometry, geometric group theory, and geometric topology.