MPS-Ascend: Triangulations of the Product of Two Simplices and Matroids from Fine Mixed Subdivisions

该奖项全部或部分根据2021年美国救援计划法案（公法117-2）资助。PI Felix Gotti被授予国家科学基金会数学和物理科学上升博士后研究奖学金（NSF MPS-Ascend），以开展与扩大STEM代表性不足的群体参与有关的研究和活动计划。Gotti博士的奖学金支持题为“MPS-上升：从精细混合细分的两个单纯形和拟阵的乘积的三角剖分”的研究项目，在赞助科学家的指导下。该奖学金的主办机构是马萨诸塞州理工学院，赞助科学家是Alex Postnikov博士。Gotti博士计划在他先前研究的基础上，研究与两个单形乘积的三角剖分和规则四面体的精细混合细分有关的代数组合学问题。在这项工作中，PI旨在解决Postnikov题为“Permutohedra，associahedra，and beyond”的工作中提出的一些问题，并解决与菱形镶嵌有关的一些问题（即，二维精细混合细分），在Ardila和Billey的题为“Flag arrangements and triangulations of product of simplices”的作品的结尾处陈述。PI的扩大参与计划包括卫星研究项目的设计，旨在将数学研究带给年轻的高度积极的学生，并指导来自STEM服务不足社区的学生。沿着适当的指导努力，这将有助于对这些学生的职业生涯产生重大的积极影响。此外，PI还将通过参与和领导MIT-PRIMES项目，向高中生提供服务。MIT-PRIMES是由NSF资助的数学和计算机科学研究项目，由麻省理工学院为高中生提供。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

This award is funded in whole or in part under the American Rescue Plan Act of 2021 (Public Law 117-2). PI Felix Gotti is awarded a National Science Foundation Mathematical and Physical Sciences Ascending Postdoctoral Research Fellowship (NSF MPS-Ascend) to conduct a program of research and activities related to broadening participation by groups underrepresented in STEM. This fellowship to Dr. Gotti supports the research project entitled "MPS-Ascend: Triangulations of the Product of Two Simplices and Matroids from Fine Mixed Subdivisions", under the mentorship of a sponsoring scientist. The host institution for the fellowship is the Massachusetts Institute of Technology, and the sponsoring scientist is Dr. Alex Postnikov.Building on his prior research, Dr. Gotti plans to investigate problems in algebraic combinatorics related to triangulations of products of two simplices and fine mixed subdivisions of regular tetrahedra. In this work, the PI aims to address some questions posed in Postnikov's work entitled "Permutohedra, associahedra, and beyond" and to settle down some problems related to lozenge tilings (i.e., two-dimensional fine mixed subdivisions) that are stated at the end of Ardila and Billey’s work titled “Flag arrangements and triangulations of product of simplices”. The PI's broadening participation plans include the design of satellite research projects aimed to bring research in mathematics to young highly-motivated students and to mentor students from under-served communities in STEM. Along with appropriate mentoring efforts, this will contribute towards a significant positive impact on these students' careers. Additionally, the PI will engage in outreach to high school students through involvement and leadership in MIT-PRIMES, an NSF-funded research program in Mathematics and Computer Sciences offered by MIT for high-school students.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.