I was an undergraduate math major at theUniversity of Maryland, where I did some work in theExperimental Geometry Lab, where I was interested in geometric structures and in dynamical systems arising from constructions in classical geometry. I was a graduate student atStony Brook, where I learned low dimensional topology and geometry, including hyperbolic geometry and Teichmüller theory. I spent two years visitingYaleand completed my dissertation under the direction ofYair Minsky. My dissertation was interested in the dynamical behavior of billiards in polygons and connections to Teichmüller theory. I received my PhD in 2006 fromStony Brook. I spent a little over three years as a Boas Assistant Professor atNorthwestern, where I learned Dynamical systems and Ergodic theory. I came to City College in the spring of 2010. City College and CUNY have offered me the opportunity to continue to develop my mathematical background, to teach interesting classes, and to interact with interesting students.

I study dynamical systems defined by piecewise continuous maps which preserve some nice structure (such as a metric) away from their discontinuities on the phase space. This subject is frequently motivated by connections to geometry. Indeed the simplest such systems, interval exchange maps, are closely related to Teichmüller theory. For many nice spaces, the group of isometries of a space is quite rigid making a dynamical analysis of the action of an isometry uninteresting. By considering piecewise continuous isometries, we obtain a richer class of dynamical systems which give rise to new dynamical phenomena. The goal of his research is to better understand these systems from a topological or ergodic theoretic point of view.