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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link="#467886" vlink="#96607D" style='word-wrap:break-word'><div class=WordSection1><p class=MsoNormal style='background:white'><span style='color:black'><a href="https://statistics.yale.edu/" title="Department of Statistics and Data Science
"><span style='font-size:22.0pt;font-family:"Arial",sans-serif;color:#286DC0;text-decoration:none'><img border=0 width=150 height=49 style='width:1.5625in;height:.5104in' id=logo src="cid:image001.jpg@01DB61A9.8909F4E0" alt="Department of Statistics and Data Science
"></span></a></span><span style='font-family:"Arial",sans-serif;color:black;mso-ligatures:none'> </span><span style='font-size:12.0pt;color:black'><a href="https://statistics.yale.edu/" title=Home><b><span style='font-size:22.0pt;font-family:"Arial",sans-serif;color:#286DC0;mso-ligatures:none'>Department of Statistics and Data Science </span></b></a></span><b><i><u><span style='font-size:22.0pt;font-family:"Arial",sans-serif;color:#286DC0;mso-ligatures:none'> <o:p></o:p></span></u></i></b></p><p class=MsoNormal><span style='font-family:"Arial",sans-serif;mso-ligatures:none'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif;mso-ligatures:none'>Theo McKenzie, Stanford University <o:p></o:p></span></p><p class=MsoNormal><!--[if gte vml 1]><v:shapetype id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f">
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</v:shape><![endif]--><![if !vml]><img width=136 height=163 style='width:1.4166in;height:1.6979in' src="cid:image003.jpg@01DB61AA.43900C50" align=left hspace=12 v:shapes="Picture_x0020_2"><![endif]><span style='font-size:12.0pt;font-family:"Arial",sans-serif;mso-ligatures:none'>Date: Monday, January 13, 2025<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif;mso-ligatures:none'>Time: 12:00PM to 1:00PM<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif;mso-ligatures:none'>Location: Kline Tower, 13th Floor, Rm. 1327A <a href="http://maps.google.com/?q=219+Prospect+Street%2C+New+Haven%2C+CT%2C+06511%2C+us">See map</a> <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif;mso-ligatures:none'>219 Prospect Street<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif;mso-ligatures:none'>New Haven, CT 06511<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif;mso-ligatures:none'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif;mso-ligatures:none'>Webcast: <a href="https://yale.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=2b4393dd-4e98-41d0-b025-b233012bccf5">https://yale.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=2b4393dd-4e98-41d0-b025-b233012bccf5</a> <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif;mso-ligatures:none'><a href="https://virtualmath1.stanford.edu/~theom/">Website</a><o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif;mso-ligatures:none'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif;mso-ligatures:none'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif;mso-ligatures:none'>Random Matrices as a Model of Discrete Quantum Chaos<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif;mso-ligatures:none'><o:p> </o:p></span></p><p class=MsoNormal><b><span style='font-size:12.0pt;font-family:"Arial",sans-serif;mso-ligatures:none'>Information and Abstract: <o:p></o:p></span></b></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif;mso-ligatures:none'>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.<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif;mso-ligatures:none'> <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif;mso-ligatures:none'>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.<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif;mso-ligatures:none'><o:p> </o:p></span></p><p class=MsoNormal><b><span style='font-size:12.0pt;font-family:"Arial",sans-serif;mso-ligatures:none'>Speaker bio: </span></b><span style='font-size:12.0pt;font-family:"Arial",sans-serif;mso-ligatures:none'>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.<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif;mso-ligatures:none'> <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif;mso-ligatures:none'> <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif;mso-ligatures:none'>Lunch at 11:30am in room 1307<br>Talk at 12:00-1:00pm in room 1327A<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif;mso-ligatures:none'><o:p> </o:p></span></p><p class=MsoNormal><i><span style='font-size:12.0pt;font-family:"Calibri",sans-serif;mso-ligatures:none'><o:p> </o:p></span></i></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:black;mso-ligatures:none'>For more details and upcoming events visit our website at </span><span style='font-size:12.0pt'><a href="https://statistics.yale.edu/calendar"><span style='font-family:"Arial",sans-serif;color:#467886;mso-ligatures:none'>https://statistics.yale.edu/calendar</span></a></span><span style='font-size:12.0pt;font-family:"Arial",sans-serif;mso-ligatures:none'>. </span><span style='font-size:12.0pt;mso-ligatures:none'><o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Arial",sans-serif;mso-ligatures:none'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:18.0pt;font-family:"Arial",sans-serif;mso-ligatures:none'>Department of Statistics and Data Science<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:9.0pt;font-family:"Arial",sans-serif;color:black;mso-ligatures:none'>Yale University<br>Kline Tower<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:9.0pt;font-family:"Arial",sans-serif;color:black;mso-ligatures:none'>219 Prospect Street<br>New Haven, CT 06511<o:p></o:p></span></p><p class=MsoNormal><a href="https://statistics.yale.edu/"><span style='color:#467886'>https://statistics.yale.edu/</span></a><o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p></div></body></html>