As I am still working toward my dissertation, most of my work has not yet reached the preprint stage. Nonetheless, here are a two papers that will come out of my dissertaion and one in an area of side interest that is nearing completion:
Symplectic and Orthogonal Analogues of Determinantal Ideals - While investigating symplectic or orthogonal representations of so called symmetric quivers, we attempt to study the algebraic geometry of orbits closures. When the quiver is symmetric equioriented $A_3$, the coordinate rings of these orbits simultaneously extend the notions of determinantal ideals and ideals defined by symmetric or antisymmetric matrices with a specified rank. We obtain resolutions and answer normality and rationality questions.
Codimension Formulas for Orbits of Representations of Symmetric Quivers - In this article we present the notion of symmetric quiver and establish results that parallel basic facts in the study of standard quivers. In particular, we describe two formulas to calculate the codimension of the orbit closures within the affine symmetric representation space.
Galois Theory in Algebraic Discrete Dynamical Systems - We consider a discrete dynamical system defined be iterating a polynomial $P\in k[x]$ over points in $\bar{k}$. Due to the dynamics of the system, the Galois group of the polynomial whose roots are the $n$ cycles is a wreath product much smaller than the full symmetric group on the roots.
Talks and Presentations
Symplectic and Orthogonal Analogues of Determinantal Ideals, AMS Special Session in Eastern Region Conference, 2002.
Orbits of Symmetric Quiver Representations, Northeastern University, 2001.
Algebra of Discrete Dynamical Systems, Eastern Nazarene College, 2001.