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

Gotti, Felix, Berkeley CA

Investigators

Abstract

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.