Events
FDS Statistics & Data Science Seminar
Random Matrices as a Model of Discrete Quantum Chaos
 |
Speaker: Theo McKenzie (Stanford ) Stanford Science Fellow Stanford University Monday, January 13, 2025 11:30AM - 1:00PM Lunch at 11:30am in room 1307
Talk at 12:00-1:00pm in room 1327A Location: Yale Institute for Foundations of Data Science, Kline Tower 13th Floor, Room 1327, New Haven, CT 06511 and via Webcast: https://yale.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=2b4393dd-4e98-41d0-b025-b233012bccf5 |
Speaker bio: Theo McKenzie is a Stanford Science Fellow in the Department of Mathematics. From 2022 to 2023, he served as an NSF MPS-Ascend Postdoctoral Fellow at Harvard. Between 2017 and 2022, he pursued his Ph.D. at UC Berkeley, where he had the privilege of being advised by Nikhil Srivastava and Luca Trevisan. His research focuses on the spectral geometry of discrete systems, with broader interests in analysis and probability, particularly in questions inspired by statistical physics and computer science. Prior to his doctoral studies, McKenzie earned his bachelor’s degree from Harvard and spent two years working as a trader.
Information and Abstract: The spectral theory of random matrices provides powerful tools for analyzing high-dimensional data in statistical contexts. Seventy years ago, Nobel Prize-winning physicist Eugene Wigner observed that the spectra of heavy nuclei resemble those of random matrices. This observation not only advanced our understanding of the quantum chaos of these large atoms but also inspired significant mathematical development in random matrix theory through techniques adapted from physics.
This talk provides an overview of the historical evolution of this field and highlights recent advances, including work with applications to community detection and error-correction. I will focus on a result that gives the limiting distribution of the largest eigenvalues of the adjacency matrix of a randomly selected regular graph, which proves the existence of optimal spectral expanders of every degree. These findings offer new insights into the interplay between randomness and structure in discrete systems.
Add To: Google Calendar | Outlook | iCal File
Submit an Event
Interested in creating your own event, or have an event to share? Please fill the form if you’d like to send us an event you’d like to have added to the calendar.