MPS-Ascend: Topics in Low-Dimensional Topology and Heegaard Floer Theory

该奖项的全部或部分资金来自《2021年美国救援计划法案》(公法117-2)。Pi Biji Wong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)，以开展一项与扩大STEM中代表性不足群体的参与相关的研究和活动。与王博士的这笔奖学金支持一位赞助科学家指导的名为“MPS-Ascend：低维拓扑和Heegaard Floer理论的主题”的研究项目。该奖学金的主办机构是杜克大学，赞助科学家是亚当·莱文博士。在她先前研究的基础上，PI计划使用边界弗洛尔理论来研究卫星结的细度以及三个轨道不变量的分类。其他项目包括使用Heegaard Floer同调来理解环上分支的三个球面的双覆盖，以及在环的背景下推广切片带状猜想。为了扩大参与，PI计划在HBCU(包括北卡罗来纳中央大学)合作建立虚拟定向阅读项目，帮助为北卡罗来纳州地区的少数族裔女性数学家组织一个辅导小组，并与数学联盟网络以及R1数学部门建立合作伙伴关系。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势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 Biji Wong 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. Wong supports the research project entitled "MPS-Ascend: Topics in Low-Dimensional Topology and Heegaard Floer Theory," under the mentorship of a sponsoring scientist. The host institution for the fellowship is Duke University, and the sponsoring scientist is Dr. Adam Levine.Building on her prior research, the PI plans to use bordered Floer theory to study sliceness of satellite knots as well as categorification of invariants of three-orbifolds. Other projects include using Heegaard Floer homology to understand double covers of the three-sphere branched over links and generalization of the slice-ribbon conjecture in the setting of links. To broaden participation, the PI plans to collaboratively set up virtual Directed Reading Programs at HBCUs, including North Carolina Central University, help organize a mentoring cluster for minority women mathematicians in the North Carolina area, and form partnerships with the Math Alliance network as well as R1 mathematics departments.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.