Alexander Jon Stathis

About Me

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*.

Click here for my curriculum vitae.

I am an avid climber, and I climb in many of the locations that I visit. Keep up with those adventures on my Instagram or via my profile on Mountain Project.

Research

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.

- Intersection Theory on the Hilbert Scheme of Points in the Projective Plane Ph.D. Thesis, 2017
- pieri.py A library of Python3 functions which compute the intersection of the divisor H with any MS basis element
- compcodim.py A library of Python3 functions which compute the intersections of complementary codimension MS basis elements
- An Algorithm for Intersections on the Hilbert Scheme of Points in the Projective Plane
*Communications in Algebra*, 2017.

© Alexander J Stathis

Last Updated: August 30th, 2017.