A Study of Hypersurfaces in General Position Inspired by Frobenius

University Of Kansas Center For Research Inc, Lawrence KS

Investigators

Abstract

This is a project in commutative algebra, which, roughly speaking, is the study of systems of polynomials equations. Polynomial equations, and the geometric objects that that these equations describe, are fundamental, both in pure and applied mathematics, but also in computer science, physics, biology, and chemistry. The project will study the nature of such systems of equations, with an emphasis on understanding the subtle ways in which they can fail to be smooth, or regular. The principal investigator will continue to mentor students that are underrepresented in the mathematical sciences. More precisely, the project team will study the singularities of algebraic varieties. The research seeks to draw, and strengthen, connections among many areas of mathematics, including prime characteristic commutative algebra, classical singularity theory, birational algebraic geometry, polyhedral geometry, and the theory of differential operators. This project places an emphasis on polynomial equations that lie in general position, as well as on explicit computations. This project is jointly funded by the Algebra and Number Theory program (ANT) and the Established Program to Stimulate Competitive Research (EPSCoR). This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.