I completed my bachelor's degrees in computer science and mathematics at the University of California at Santa Cruz in 2011. I decided to pursue mathematics after flirting with a career as a software developer, and completed my doctorate in mathematics at the University of Illinois at Chicago in 2017.
Outside of mathematics, I am an avid rock climber.
I am an algebraic geometer interested in questions about the intersection theory and birational geometry of moduli spaces. My thesis establishes an intuitive geometric description of intersection products on the Hilbert scheme of points in the projective plane in a basis defined by incidence conditions on the points. The basis admits a nice index set via partitions, and my results attempt to provide a description analogous to Schubert calculus for the Grassmannian in this basis.
Intersection theory is a useful tool for computing cones in the spaces of cycles on a space. I would like to investigate questions about the birational geometry of the Hilbert scheme and related spaces via the results developed in my thesis. In pparticular, very little is known about the positivity of higher codimension cycles on these spaces.