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

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)。派·乔纳森·约翰逊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。约翰逊博士的这一奖学金支持了一位赞助科学家的指导下的名为“MPS-Ascend：双向有序性、纤维结和循环分支覆盖”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，这个项目包括一个新的猜想，将纤维和两桥纽结群的双序性与纽结的循环分支覆盖的L空间猜想条件联系起来，利用纽结的亚历山大多项式来刻画双序性，以及产生双可序3-流形群的例子的新方法。为了扩大参与，PI计划在俄克拉荷马州立大学建立一个定向阅读项目，重点是从代表不足的群体中招收学生，特别是该大学庞大的美国原住民人口。另一项贡献将是创建面向本科生和早期职业数学家的可公开访问的在线视频，涵盖低维拓扑结构中的广泛主题。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 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.