Post-Doc Assistant Professor
1844 East Hall
Phone: (734) 936-0085
- Algebra/Algebraic Geometry
I enjoy many forms of algebra, which in modern math means the study of rules for combining mathematical expressions, such as multiplying polynomials or composing symmetries. One of my favorite aspects of algebra is 'algebraic geometry', which is the relation between the algebraic properties of a system of equations, and the geometry of its set of solutions. My preferred type of research is finding natural explanations for unexpectedly nice phenomena.
Recently, my research has focused on cluster algebras, which generalize the algebras of functions on many notable spaces, such as spaces of matrices, reductive Lie groups, Grassmannians and Teichmueller space. Roughly speaking, these algebras have many special coordinate systems - called 'clusters' - together with a recursive rule which allows any cluster to be reconstructed from any other cluster. This simple setup has far-reaching consequences, which includes good geometric properties in many cases, but not all. Part of my research has been the introduction and investigation of 'locally acyclic cluster algebras', a definition intended to characterize those cluster algebras which are geometrically well-behaved.