Postdoctoral Fellowship: MPS-Ascend: Topics in Analytic Number Theory

Jones, Edna Luo, Piscataway NJ

Investigators

Abstract

Dr. Edna Jones 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 "MPS-Ascend: Topics in Analytic Number Theory and Math Outreach." The project activities will be conducted at the host institution, Tulane University, under the mentorship of Dr. Olivia Beckwith. The PI will build upon her research in analytic number theory. The PI plans to prove results on representing integers as bends of n-spheres in integral Kleinian sphere packings by using the circle method with a Kloosterman refinement, the spectral theory of automorphic forms, expander graphs, homogeneous dynamics, and analytic estimates on exponential sums. The PI is also planning to continue research computing moments of L-functions associated with Artin-Schreier curves by obtaining better estimates on sums. The PI also plans to analyze the asymptotics of coefficients of real-analytic modular forms using spectral decompositions, special functions, and the circle method. The PI plans to work with various organizations (such as STEM NOLA, Tulane University’s Girls in STEM (GiST) at Tulane and Boys at Tulane in STEM (BATS), and Math for All in New Orleans) to broaden participation in STEM by having positive STEM interactions with the population of New Orleans. 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.