Postdoctoral Fellowship: MPS-Ascend: Topological Enrichments in Enumerative Geometry

博士后奖学金：MPS-Ascend：枚举几何中的拓扑丰富

• 批准号: 2402099
• 负责人: Candace Bethea
• 金额: $ 30万
• 依托单位: Bethea, Candace
• 依托单位国家: 美国
• 项目类别: Fellowship Award
• 财政年份: 2024
• 资助国家: 美国
• 起止时间: 2024-05-01 至 2027-04-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2402099&HistoricalAwards=false
• 关键词: Postdoctoral; Fellowship; MPS; Ascend; Topological

Dr. Bethea is awarded a National Science Foundation Mathematical and Physical Sciences Ascending Postdoctoral Research Fellowship (NSF MPS-Ascend) to conduct a program of research, education, and activities related to broadening participation by groups underrepresented in STEM. This fellowship supports the research project entitled "Topological Enrichments in Enumerative Geometry". The project activities will be conducted at the host institution, Duke University, under the mentorship of Dr. Kirsten Wickelgren.The goal of this research proposal is to investigate equivariant enumerative geometry, a subject which centers around using invariants from equivariant homotopy theory to generalize classical enumerative results, probing symmetries through group actions. The PI will accomplish this by: (1) Defining and computing equivariant Gromov-Witten invariants, and (2) Investigating local equivariant enrichments in the Burnside ring. This represents an ambitious but natural continuation of her previous work in equivariant curve counting. The PI will also develop pre-college enrichment activities to expose underrepresented minority students to inspiring mathematics and mathematical careers.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.

Bethea 博士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)，用于开展与扩大 STEM 代表性不足群体的参与相关的研究、教育和活动计划。该奖学金支持题为“枚举几何中的拓扑丰富”的研究项目。该项目活动将在主办机构杜克大学进行，并在 Kirsten Wickelgren 博士的指导下进行。该研究计划的目标是研究等变枚举几何，该学科的核心是利用等变同伦理论中的不变量来推广经典几何。枚举结果，通过群体行动探索对称性。 PI 将通过以下方式实现这一目标：(1) 定义和计算等变 Gromov-Witten 不变量，以及 (2) 研究 Burnside 环中的局部等变富集。这代表了她之前在等变曲线计数方面的工作的雄心勃勃但自然的延续。 PI 还将开展大学前的丰富活动，让代表性不足的少数族裔学生接触鼓舞人心的数学和数学职业。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力优点和更广泛的影响审查标准进行评估，被认为值得支持。