MPS-Ascend: Understanding Khovanov Homology Through Configuration Spaces

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蒙托亚-维加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。蒙托亚-维加博士的奖学金支持题为“MPS-Ascend：通过配置空间理解Khovanov同源性”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纽约研究生中心，赞助科学家是纽约市立大学皇后学院的荣永武博士。这个项目的重点是研究使用配置空间的链接不变量的构建，目标是提供Khovanov同调的拓扑结构。PI蒙托亚-维加将结合荣博士开发的霍瓦诺夫型同源性理论。图的多项式，如色多项式，Tutte多项式，和彭罗斯多项式，预计将发挥关键作用。除了研究目标，作为第一代拉丁裔数学家，PI受益于对学生和来自代表性不足群体的早期职业研究人员所面临的挑战的洞察力。通过会议组织和积极鼓励以及指导，以及通过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。这个奖项反映了NSF的法定使命，并已被认为是值得支持的评估使用基金会的智力价值和更广泛的影响审查标准。

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.