MPS-Ascend: Understanding Khovanov Homology Through Configuration Spaces

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 Montoya-Vega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。Montoya-Vega博士的研究项目名为“MPS-Ascend：通过配置空间理解Khovanov同源性”，由一位赞助科学家指导。该奖学金的主办机构是纽约市立大学研究生中心，赞助科学家是纽约市立大学皇后学院的容永武博士。这个项目的重点是研究链路不变量的结构使用位形空间与提供Khovanov同调的拓扑结构的目标。PI Montoya-Vega将纳入荣博士开发的khovanov型同源理论。图多项式的分类，如色多项式、图特多项式和彭罗斯多项式，有望发挥关键作用。除了研究目标，作为第一代拉丁裔数学家，PI受益于对来自代表性不足群体的学生和早期职业研究人员所面临的挑战的洞察力。通过组织会议，积极鼓励和指导，以及提供一个成功的榜样，他的目标是扩大参与数学和物理科学。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 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.