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

Bethea博士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），以开展与扩大STEM中代表性不足的群体参与有关的研究，教育和活动计划。该奖学金支持题为“枚举几何的拓扑丰富”的研究项目。项目活动将在主办机构杜克大学进行，由Kirsten Wickelgren博士指导。本研究的目标是研究等变枚举几何，这是一个围绕使用等变同伦理论中的不变量来推广经典枚举结果，通过群作用探索对称性的主题。PI将通过：(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来实现这一目标。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，让未被充分代表的少数民族学生接触鼓舞人心的数学和数学事业。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.