Postdoctoral Fellowship: MPS-Ascend: Orbit Method and Analysis of Automorphic Forms

Dr. Trajan Hammonds is awarded a National Science Foundation Mathematical and Physical Sciences Ascending Postdoctoral Research Fellowship (NSF MPS-Ascend) to conduct a program of research and broader impact activities. This fellowship supports the research project entitled "Orbit Method and Analysis of Automorphic Forms". The project activities will be conducted at the host institution, Massachusetts Institute of Technology, under the mentorship of Dr. Larry Guth. This project aims to further explore and investigate the connection between the orbit method and the analysis of automorphic forms, via microlocal and harmonic analysis. The PI plans to tackle a number of problems that may be amenable to techniques in analysis. This includes proving a refinement of the microlocal Op-calculus to effectively compute matrix coefficients of weight vectors leading to bounds for spherical functions or bounds for the sup norm of automorphic forms. Building on previous work on L4 norms of Maass forms, the PI will also investigate L4 norms on compact quotients and Lp norms for p larger than 4. The PI also plans to advise undergraduate research projects and mentor undergraduate and graduate math students alike as well as leading learning seminars highlighting the connections between number theory and analysis. 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.