Nancy Jauregui
The aim of this project is to develop, implement, and assess a new model for undergraduate involvement in research, targeting first and near-first generation to college STEM majors who attend community colleges. First-generation college students are only slightly underrepresented in terms of initial STEM enrollment, but much less likely to complete their degree. Near-first generation students are those who have a parent with a four-year degree, but who have little to no knowledge about success in higher education in the U.S. (e.g., foster children, children of immigrants). Students from both […]
Aidan Backus
Over the summer, we propose to investigate the root multiplicities of (generalized) Kac-Moody Algebras. Our plan is to create an open-source computer package that allows for the computation of root multiplicities of Kac-Moody algebras, building upon the existing tools available to computational mathematicians, for instance, the popular library sage-math. Once we have developed and verified this package against known tables of root multiplicities, we aim to start investigating the root multiplicities of simple graphs, and attempt to address some outstanding conjectures on the distributions of root multiplicities. A greater understanding […]
Yining Liu
In our research, we will use toric geometry to study the cohomological structure of complex Grassmannians. The cohomology ring of a Grassmannian varieties is described by the Littlewood-Richardson rule. One of the main open questions in Schubert calculus concerns the generalization of the Littlewood-Richardson rule to flag varieties. Such a generalization is highly desirable, because it is a manifestly positive formula that can be applied to other areas: in algebraic geometry, it helps describe complicated intersections; in representation theory, it helps to find irreducible, direct-sum decompositions of tensor products; in […]