Research interests

My research is in commutative algebra, and is motivated by connections with birational algebraic geometry, the theory of differential operators, classical singularity theory, and convex geometry. I am especially interested in applications of the Frobenius endomorphism and related prime characteristic methods, local cohomology, and convexity to the study of algebraic varieties.

Acknowledgments

My research is partially supported by the National Science Foundation (NSF) through the grant DMS-1902321. In the recent past, my research was partially supported by the American Institute of Mathematics through an AIM SQuaRE award for collaborative research, the KU Office of Research through a KU Research GO Award, the KU New Faculty General Research Fund, and the NSF through the grant DMS-1600702, and through the Mathematical Sciences Postdoctoral Research Fellowship DMS-1304250.

Software development

I co-authored the following packages for Macaulay2 (M2), a software system devoted to supporting research in algebraic geometry and commutative algebra. These packages focus on explicit computation in prime characteristic, and include implementations of some of the algorithms developed in my research papers, but also a lot more.

Papers