I am an RTG Postdoctoral Research and Teaching Associate at the University of Georgia for the academic years 2017-18 and 2018-19.
I received my Ph.D. in mathematics from the University of Illinois at Chicago in 2017. My adviser was İzzet Coşkun. My thesis was titled Intersection Theory on the Hilbert Scheme of Points in the Projective Plane.
I am an algebraic geometer interested in questions about the birational geometry and intersection theory 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 analgous 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 particular, very little is known about the "positivity" of higher codimension cycles on these spaces.
© Alexander J Stathis
Last Updated: August 30th, 2017.