NSF Award
2418805
Solving polynomial equations with multiple variables is a common problem across the sciences, with applications ranging from robotics to mathematical biology. In this project, the PI will examine such problems in the realm of commutative algebra through the study of minimal free resolutions of ideals in a polynomial ring. Specifically, the PI will focus on monomial ideals, which are key to understanding the structure of any ideal, a central topic in commutative algebra and algebraic geometry. The second part of this project is the study of parking functions, a concept originating in computer science. The PI will examine two novel variations of parking functions: Stirling permutations and tiered parking functions. The last part of this project is the PI’s ongoing work "Meet a Mathematician," a video series aimed at broadening the participation of historically excluded and underrepresented groups in the mathematical sciences.<br/><br/>The PI’s work on monomial ideals will focus on their algebraic invariants that arise from minimal free resolutions. Specifically, the PI will investigate algebraic invariants of monomial ideals associated to graphs and express these invariants in terms of combinatorial data of graphs. The PI’s work on parking functions will focus on developing a framework to study Stirling permutations and tiered parking functions. A special focus will be given to the enumeration of these parking functions and the geometry of their associated polytopes. Lastly, the PI will work on initiatives related to "Meet a Mathematician,” with the goal of broadening participation in the mathematical sciences from local to international levels. Specifically, the PI will continue the "Meet a Mathematician” video series, organize an annual inclusive math conference at Bryn Mawr College for students in the Philadelphia area, and host storytelling events at national math conferences.<br/><br/>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.
