Assistant Professor Federico Galetto (Dept. of Mathematics and Statistics) was award an NSF Grant for $123,410 for "Finite Group Actions on Free Resolutions" for 2022-2025.
Brief Abstract: Solving systems of polynomial equations is a central problem in algebra with many practical applications. The solutions of a system can be regarded as a geometric object, called a variety, leading to a fruitful interplay between algebra and geometry. Varieties can be described by means of numerical parameters, such as their dimension, a measure of size, their degree, a measure of complexity, and more generally their so-called Betti numbers, which provide additional information of algebraic and geometric significance. In this project, the PI aims to describe as explicitly as possible the Betti numbers of some well-known systems of polynomial equations by making use of the inherent symmetries of the underlying varieties. The study will rely on computer algorithms previously developed by the PI for this specific purpose. The grant provides support for graduate students, who will be involved in collecting and analyzing of data, thus providing newer generations of scientists with a diverse background an opportunity to experience hands-on research in addition to learning some advanced mathematics.