Math Research

Current Research

I'm a math graduate student at the University of Oregon studying algebraic geometry under the guidance of Nicolas Addington. My work focuses on computing Hasse-Weil zeta functions of smooth hypersurfaces and complete intersections in Grassmannians using $p$-adic cohomology.

My code for these computations is available on GitHub.

Hodge Diamond Calculator

This applet computes the Hodge diamond of a few classes of interesting varieties over $\mathbb C$, such as complete intersections, abelian varieties, and Grassmannians.

Preset Examples

Complete Intersection Calculator

Dimension of Projective Space ($n$):

Number of Hypersurfaces ($k$):

Hodge Diamond

The Hodge diamond will be displayed here.

Preset Examples

Abelian Variety Calculator

Genus ($g$):

Hodge Diamond

The Hodge diamond will be displayed here.

Grassmannian Calculator

Dimension of Ambient Space ($n$):

Dimension of Subspace ($k$):

Number of Hypersurfaces ($r$):

Hodge Diamond

The Hodge diamond will be displayed here.

Past Work

A few years ago I computed some blowups of toric varieties. Some of the code is available here.