Swatee Naik
$100,000
McKenzie, Theo R
California
Mathematical and Physical Sciences (MPS)
This award is funded in whole or in part under the American Rescue Plan Act of 2021 (Public Law 117-2). PI Theo McKenzie 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. McKenzie supports the research project entitled "MPS-Ascend: Eigenvector Statistics of the Adjacency Operator of Graphs", under the mentorship of a sponsoring scientist. The host institution for the fellowship is Harvard University, and the sponsoring scientist is Dr. Hong-Tzer Yau.<br/><br/>The project's goal is to study the structure of eigenvectors of operators on graphs. The PI will work in three research directions: deduce eigenvector and eigenvalue statistics such as the number of nodal domains of random and semi-random graphs using the combinatorial structure of the graph to prove eigenvector delocalization; bound the number of eigenvalues near the edge of the spectrum for operators on graphs and manifolds using PI's prior research; and generalize known results in quantum ergodicity to graph families with arbitrary limits to further elucidate the connection between eigenvector statistics of a graph family and those of the infinite limit. PI's broadening participation activities are two-fold. One, the PI will leverage his experience as a lead instructor at the associate degree program at San Quentin State Prison, to teach and introduce a more advanced curriculum in the college programs at prisons in Massachusetts, that have a high population of racial minorities. This project aims to directly help those who are incarcerated learn higher level math and thereby gain agency. Second, using his own experience as a Black mathematician, create a community of postdocs and graduate students from underrepresented backgrounds at Harvard. This group will interact with each other and work on personal development activities thereby creating a welcoming environment for researchers.<br/><br/>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.