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

该奖项全部或部分由《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提升博士后研究奖学金（NSF MPS-Ascend），以开展与扩大STEM中代表性不足的群体参与相关的研究和活动计划。Gotti博士的研究项目名为“MPS-Ascend：精细混合细分的两个单形和拟形乘积的三角剖分”，由一位赞助科学家指导。该奖学金的主办机构是麻省理工学院，赞助科学家是亚历克斯·波斯特尼科夫博士。在他之前研究的基础上，Gotti博士计划研究代数组合学中与两个简单积的三角剖分和正四面体的精细混合细分相关的问题。在这项工作中，PI旨在解决Postnikov的作品“Permutohedra， associahedra和beyond”中提出的一些问题，并解决一些与菱形平铺（即二维精细混合细分）相关的问题，这些问题在Ardila和Billey的作品“单质积的标志排列和三角测量”的最后陈述。PI扩大参与的计划包括设计卫星研究项目，旨在将数学研究带给高度上进心的年轻学生，并指导来自服务不足社区的学生学习STEM。加上适当的指导，这将对这些学生的职业生涯产生重大的积极影响。此外，PI将通过参与和领导MIT- primes（由美国国家科学基金会资助的麻省理工学院为高中生提供的数学和计算机科学研究项目），与高中生进行接触。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识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.