## Summary of Research

The algebra research group focuses on infinite group theory, algebraic geometry, commutative algebra, and combinatorics.

## Faculty Members

### Ulysses Alvarez

Dr. Alvarez’s is currently interested in geometric interpretations of certain features pertaining to cluster algebras, such as viewing the coefficients of cluster variables as Euler characteristics of appropriate quiver Grassmannians and understanding cluster algebras coming from triangulations of surfaces.

Find Dr. Alvarez’s contact information in the department directory.

### Jon Corson

Professor Corson’s research is in geometric ring theory.

Find Dr. Corson’s contact information in the department directory.

### Kyunglong Lee

Dr. Lee’s research lies in the intersection of algebra, combinatorics, geometry, topology, and physics. The algebraic objects he is particularly interested in include cluster algebras, MacDonald polynomials, and Kazhdan-Lusztig polynomials. All of these are motivated by theoretical physics, and have been studied in terms of (co)homologies, algebraic combinatorics, and topological cell decompositions. He uses tools from a wide variety of mathematical areas, including algebraic geometry, commutative algebra, non-commutative algebra, and representation theory.

Find Dr. Lee’s publications on MathSciNet and ArXiv.

Find Dr. Lee’s contact information in the department directory.

### Thomas Polstra

Dr. Polstra’s research lies in commutative algebra and algebraic geometry.

Find Dr. Polstra’s contact information in the department directory.