MPS-Ascend: Understanding Khovanov Homology Through Configuration Spaces

Montoya-Vega, Gabriel Jaime, Washington DC

Investigators

Abstract

This award is funded in whole or in part under the American Rescue Plan Act of 2021 (Public Law 117-2). PI Montoya-Vega 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 broaden participation by groups underrepresented in STEM. This fellowship to Dr. Montoya-Vega supports the research project entitled "MPS-Ascend: Understanding Khovanov Homology Through Configuration Spaces", under the mentorship of a sponsoring scientist. The host institution for the fellowship is City University of New York (CUNY) Graduate Center, and the sponsoring scientist is Dr. Yongwu Rong at Queens College, CUNY. The focus of this project is to study the construction of link invariants using configuration spaces with the goal of providing a topological construction of the Khovanov homology. PI Montoya-Vega will incorporate the Khovanov-type homology theories developed by Dr. Rong. The categorifications of graph polynomials such as the chromatic polynomial, the Tutte polynomial, and the Penrose polynomial, are expected to play a key role. In addition to the research goals, as a first-generation Latino mathematician, the PI benefits from an insight to the challenges faced by students and early career researchers from underrepresented groups. Through conference organization and active encouragement as well as mentoring, as well as by providing a successful role model, he aims to broaden participation in mathematical and physical sciences. 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.