My graduate research interests were in computational and numerical algebraic geometry. Specifically I found myself working with toric varieties and toric degenerations, numerical homotopies, Khovanskii bases, Newton-Okounkov bodies, and applications to chemical reaction networks.

My Ph.D. advisor was Frank Sottile . 


Preprints

SubalgebraBases in Macaulay2

(with Michael Burr, Oliver Clarke, Tim Duff, Jackson Leaman, and Nathan Nichols)

Preprint

Macaulay2 is a software system used extensively in algebraic geometry and related fields. We revived a software package for Macaulay2 which can compute subalgebra bases. More details can be found on the software package website. 

Newton-Okounkov bodies of chemical reaction systems

(with Nida Obatake)

Preprint

More details, including links to supplemental code, can be found here. 

Publications

Polyhedral homotopies in Cox coordinates

(with Tim Duff, Simon Telen, and Thomas Yahl)

Preprint, to appear in Journal of Algebra and its Applications.

More details, including supplemental code, can be found here. Image courtesy of Simon.

Numerical homotopies from Khovanskii bases

(with Michael Burr and Frank Sottile, 2023)

Preprint. The paper is published here in Mathematics of Computation. 

Summary details, including links to supplemental code, can be found here. 

Image courtesy of Frank.

Jacobian elliptic Kummer surfaces and special function identities

(with Andreas Malmendier, 2016)

Preprint. See the paper here. 

Numerical assessment of CaOx renal calculi development in space using PBE coupled to urinary flow and species transport

(with Mohammad Kassemi and David Thompson, 2018)

See the paper here. 

Bayesian analysis for risk assessment of selected medical events in support of the Integrated Medical Model effort

(with Kelly Gilkey, Michael McRae, Aditya Kalluri, and Jerry Myers, 2012)

See the paper here.