Postdoctoral Fellowship: MPS-Ascend: Harmonic Analysis Techniques in the Study of Operators in Several Complex Variables

Sweeting, Brandon Scott, Tuscaloosa AL

Investigators

Abstract

Dr. Brandon Sweeting 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 "Harmonic Analysis Techniques in the Study of Operators in Several Complex Variables". The project activities will be conducted at the host institution, Washington University in St. Louis, under the mentorship of Dr. Brett Wick. This project aims to further the application of harmonic analysis techniques in the study of operators in several complex variables. Building on their previous work, the PI plans to investigate several problems involving a novel weighted norm inequality (and its associated class of weights) for the Bergman projection. This includes investigating general boundedness properties and their geometric implications and delving deeper into finer properties, such as the extrapolation of such estimates and factorization of corresponding weights. The broader impacts portion of this project will be felt across multiple levels. Locally, the PI will contribute to the Joint Post-baccalaureate Program (JPP) at Washington University in St. Louis, aiming to support the progression of prospective doctoral students in mathematics. Additionally, the PI will engage with the WashU Math Circle, aiming to spark interest in mathematics among younger students and increase recruitment. Regionally, the PI will collaborate with universities in the greater St. Louis area to help organize a conference targeting students in mathematics, providing a platform for scholarly exchange and collaboration. Nationally, the PI plans to collaborate with the Math Alliance as a mentor, offering guidance to students on pursuing PhD programs in mathematics. 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.