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

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 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 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.