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

职业：拟阵、多面体及其在代数和几何中的估值

基本信息

批准号：
0956178
负责人：
Federico Ardila
金额：
$ 44万
依托单位：
San Francisco State University
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2010
资助国家：
美国
起止时间：
2010-07-01 至 2016-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=0956178&HistoricalAwards=false
关键词：
CAREER Matroids polytopes their valuations

项目摘要

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.

职业：拟阵、多面体以及它们在代数和几何中的评估这项工作的驱动力是这样的哲学：纯数学和应用数学中的许多对象、关系和过程可以通过研究它们背后丰富的离散结构来最好地理解。 PI将研究数值分析（带位空间）、不变理论和代数几何（Cox-Nagata环）、分支覆盖的枚举几何（Hurwitz数）和热带几何（热带线性空间和热带均匀空间）中出现的对象。这些对象的几个重要特征被编码在（Coxeter）拟阵、多面体和估值的组合中。获得的结果将应用于箱形样条理论和系统发育学。该研究项目是旧金山州立大学-哥伦比亚组合学计划的学术支柱，该计划是这两个地点的教师和学生之间的一项新兴合作，其中大多数是代表性不足的成员数学组。该计划的目的是为两个数学服务欠缺的社区提供有影响力的研究和教学经验。通过联合课程和研究项目，学生们参与了他们的第一次国际学术经历，同时做出了认真的科学贡献。该提案由组合学和国际科学与工程办公室联合资助。