CAREER: Matroids, polytopes, and their valuations in algebra and geometry

点击翻译按钮获取中文摘要

CAREER: Matroids, polytopes, and their valuations in algebra and geometryThis work is driven by the philosophy that many objects, relationships, and procedures in pure and applied mathematics are best understood by studying the rich discrete structures underlying them. The PI will study objects arising in numerical anaylsis (zonotopal spaces), invariant theory and algebraic geometry (Cox-Nagata rings), enumerative geometry of ramified covers (Hurwitz numbers), and tropical geometry (tropical linear spaces and tropical homogeneous spaces). Several important features of these objects are encoded in the combinatorics of (Coxeter) matroids, polytopes, and valuations. The results obtained will have applications in box spline theory and phylogenetics.This research program is the academic backbone of the San Francisco State University-Colombia Combinatorics Initiative, an emerging collaboration between faculty and students in these two locations, most of whom are members of underrepresented groups in mathematics. The purpose of this initiative is to provide influential research and teaching experiences to two underserved communities in mathematics. Through joint courses and research projects, students participate in their first international academic experience, while making serious scientific contributions.This proposal is being funded jointly by Combinatorics and the Office of International Science and Engineering.