### Math Research Groups

The department has research groups in the following areas:

#### Algebra, Combinatorics and Number Theory

Our research group in Algebra, Combinatorics and Number Theory includes specialists in algebraic combinatorics, Lie algebras, algebraic number theory, and commutative algebra. Their work includes applications to mathematical physics, representation theory, algebraic geometry, and topological data analysis. There is significant interaction within this research group, and between them and the topologists.

Analysis

Our research group in Analysis works in a variety of fields, including operator theory, harmonic analysis, partial differential equations, complex analysis, functional analysis, mathematical physics, and approximation theory. Their work includes connections to image processing and geometry/topology.

#### Data Science

In order to stay at the cutting edge of data science, many of our faculty have research programs that perfectly complement our courses in the data science masters program. Areas such as machine learning and topological data analysis cross traditional boundaries of algebra, analysis, geometry and topology, and statistics.

#### Geometry and Topology

The geometry/topology group at the University at Albany conducts research in a variety of areas, e.g., geometric topology, geometric group theory, group actions on manifolds, equivariant homotopy theory, and topological data analysis.

Probability and Statistics

Research interests of faculty members in probability and statistics include probability on finite groups and other discrete structures, ergodic theory, and Bayesian inference.