MPS-Ascend: The C*-Algebraic Mackey Bijection for Real Reductive Groups

Roman, Angel R, Williamsburg VA

Investigators

Abstract

This award is funded in whole or in part under the American Rescue Plan Act of 2021 (Public Law 117-2). PI Angel Roman is awarded a National Science Foundation Mathematical and Physical Sciences Ascending Postdoctoral Research Fellowship (NSF MPS-Ascend) to conduct a program of research and activities related to broadening participation by groups underrepresented in STEM. This fellowship to Dr. Roman supports the research project entitled "The C*-Algebraic Mackey Bijection for Real Reductive Groups", under the mentorship of a sponsoring scientist. The host institution for the fellowship is Washington University in St. Louis, Missouri, and the sponsoring scientist is Dr. Xiang Tang. This project seeks to examine the Mackey bijection between tempered, irreducible unitary representations of a real reductive group and the unitary irreducible representations of its Cartan motion groups in greater detail through the theory of C*-algebras and through continuous fields of C*-algebras. Building on PI’s prior research, the PI will work with collaborators to better understand the cyclic homology of Harish-Chandra Schwartz algebras, an object of study in noncommutative geometry, using the embedding result and Mackey correspondence. The broadening participation activities are three-fold. The PI will collaborate with researchers in Puerto Rico to organize student-oriented conferences in Puerto Rico and help mentor Latin American students. Using the leadership development skills the PI used as a Taekwondo coach at Penn State, the PI will engage in graduate student and postdoctoral scholar's professional development through a working seminar on “Noncommutative geometry and Representation Theory.” Last but not the least, as a Hard-of-Hearing mathematician, the PI brings valuable insight to the issues faced by this community with transcription and captions for technical terms in mathematics. The PI will work with Gallaudet University, a premier university for the Deaf and Hard-of-Hearing with an undergraduate program in mathematics, in developing better resources. 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.