MPS-Ascend: Bi-Orderability, Fibered Knots, and Cyclic Branched Covers

该奖项的全部或部分资金根据《2021 年美国救援计划法案》（公法 117-2）提供。 PI Jonathan Johnson 被授予美国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)，用于开展一项与扩大 STEM 领域代表性不足群体的参与相关的研究和活动计划。约翰逊博士的这项奖学金支持在一位资助科学家的指导下题为“MPS-Ascend：双向可排序性、纤维结和循环分支覆盖物”的研究项目。该奖学金的主办机构是俄克拉荷马州立大学，赞助科学家是尼尔·霍夫曼博士。受 PI 过去研究的启发，该项目包括一个新颖的猜想，将纤维和双桥结群的双有序性与结的循环分支覆盖的 L 空间猜想条件联系起来，用结的亚历山大多项式描述双有序性的可能特征，以及产生双有序 3 流形群示例的新方法。为了扩大参与范围，PI 计划在俄克拉荷马州立大学创建一个定向阅读项目，重点是从代表性不足的群体中招收学生，特别是该大学大量的美国原住民群体。另一项贡献将是针对本科生和早期职业数学家创建可公开访问的在线视频，涵盖低维拓扑中的广泛主题。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力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 Jonathan Johnson 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. Johnson supports the research project entitled "MPS-Ascend: Bi-Orderability, Fibered Knots, and Cyclic Branched Covers", under the mentorship of a sponsoring scientist. The host institution for the fellowship is Oklahoma State University, and the sponsoring scientist is Dr. Neil Hoffman. Motivated by the PI’s past research, this project includes a novel conjecture linking bi-orderability of fibered and two-bridge knot groups to the L-space conjecture conditions of the cyclic branched covers of the knots, a possible characterization of bi-orderability in terms of the Alexander polynomial of knots, and new methods of producing examples of bi-orderable 3-manifold groups. For broadening participation, the PI plans to create a Directed Reading Program at Oklahoma State University, with a focus on recruiting students from underrepresented groups, particularly the university's large Native American population. An additional contribution will be to create publicly accessible online videos covering a broad range of topics in low-dimensional topology, aimed at undergraduate students and early career mathematiciansThis 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.