Goldin receives funding for collaborative project exploring calculus beyond Schubert
Rebecca Goldin, Director, Graduate Studies, Mathematical Sciences, Professor,received funding from the National Science Foundation for the project: "FRG: Collaborative Research: Calculus beyond Schubert."
Goldin and her collaborators aim to resolve long outstanding problems, develop modern extensions of Schubert calculus to concepts such as equivariant quantum K-theory, and extend algebraic structures arising in Schubert calculus to other G-varieties such as the cotangent bundle of a homogeneous space or a Hessenberg variety.
They also aim to train graduate students for research in Schubert calculus through a three-year seminar series, a two-week summer school, and a one-week research conference.
"This research project aims to resolve outstanding questions in enumerative algebraic geometry. Broadly speaking, methods for finding simultaneous solutions to multiple equations have significant implications for progress in physics, computer science, and engineering. These solutions may be expressed in terms of the intersection of certain geometric spaces. The search for exact formulas for the number of solutions in enumerative geometry is an active area of research with relations to numerous fields, including geometry, combinatorics, representation theory, complexity theory in computer science, and mirror symmetry in theoretical physics," Goldin said.
Goldin received $170,233 from NSF for this project. Funding began in Aug. 2022 and will end in late July 2025.