<html><head><meta http-equiv="content-type" content="text/html; charset=utf-8"></head><body dir="auto"><div dir="ltr"><br><br><br>Begin forwarded message:<br><br></div><blockquote type="cite"><div dir="ltr"><b>From:</b> Mat <matwimberly@uchicago.edu><br><b>Date:</b> March 28, 2022 at 12:33:14 PM CDT<br><b>To:</b> all_math@lists.uchicago.edu<br><b>Subject:</b> <b>*Correction* Colloquium: Yufei Zhao (MIT)</b><br><b>Reply-To:</b> Mat <matwimberly@uchicago.edu><br><br></div></blockquote><blockquote type="cite"><div dir="ltr">
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<title>*Correction* Colloquium: Yufei Zhao (MIT)</title>
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<span style="font-size:19px"><strong>Please note that the colloquium will take place on April 30th, 2022 at 3:00pm in Eckhart Hall Room 202.</strong></span><br>
<br>
<strong>The previous email had the incorrect date listed in the zoom details.</strong>
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<h1 class="null" style="text-align: center;display: block;margin: 0;padding: 0;color: #222222;font-family: Helvetica;font-size: 40px;font-style: normal;font-weight: bold;line-height: 150%;letter-spacing: normal;">Yufei Zhao<br>
(MIT)</h1>
<div style="text-align: center;"><strong><span style="font-size:24px">Equiangular Lines and Eigenvalue Multiplicities</span></strong></div>
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<img alt="Wednesday, March 30th" src="https://mcusercontent.com/350fc31a7f826e3b52544f33a/images/c5aa249e-0ef9-cd2f-531a-cd1f5bb65337.png" width="264" style="max-width: 1100px;padding-bottom: 0;border: 0;height: auto;outline: none;text-decoration: none;-ms-interpolation-mode: bicubic;vertical-align: bottom;" class="mcnImage" data-unique-identifier="">
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<img alt="3:00pm Central Time" src="https://mcusercontent.com/350fc31a7f826e3b52544f33a/images/c89dc4e5-9fec-405c-bbd6-fc0172874aef.png" width="264" style="max-width: 1101px;padding-bottom: 0;border: 0;height: auto;outline: none;text-decoration: none;-ms-interpolation-mode: bicubic;vertical-align: bottom;" class="mcnImage" data-unique-identifier="">
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<img alt="Eckhart Hall, Room 202" src="https://mcusercontent.com/350fc31a7f826e3b52544f33a/images/2bb0348d-2468-6419-275b-6cf348f80a63.png" width="564" style="max-width: 1200px;padding-bottom: 0;border: 0;height: auto;outline: none;text-decoration: none;-ms-interpolation-mode: bicubic;vertical-align: bottom;" class="mcnImage" data-unique-identifier="">
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<h3 style="text-align: center;display: block;margin: 0;padding: 0;color: #444444;font-family: Helvetica;font-size: 22px;font-style: normal;font-weight: bold;line-height: 150%;letter-spacing: normal;"><span style="font-size:18px"><strong>Equiangular Lines and Eigenvalue Multiplicities</strong></span></h3>
<br>
<strong>Abstract:</strong>
<p style="margin: 10px 0;padding: 0;mso-line-height-rule: exactly;-ms-text-size-adjust: 100%;-webkit-text-size-adjust: 100%;color: #757575;font-family: Helvetica;font-size: 16px;line-height: 150%;text-align: left;">Solving a longstanding problem on equiangular lines, we determine, for each given fixed angle and in all sufficiently large dimensions, the maximum number of lines pairwise separated by the given angle.</p>
<p style="margin: 10px 0;padding: 0;mso-line-height-rule: exactly;-ms-text-size-adjust: 100%;-webkit-text-size-adjust: 100%;color: #757575;font-family: Helvetica;font-size: 16px;line-height: 150%;text-align: left;">A key ingredient is a new result in spectral graph theory: the adjacency matrix of a connected bounded degree graph has sublinear second eigenvalue multiplicity.</p>
<p style="margin: 10px 0;padding: 0;mso-line-height-rule: exactly;-ms-text-size-adjust: 100%;-webkit-text-size-adjust: 100%;color: #757575;font-family: Helvetica;font-size: 16px;line-height: 150%;text-align: left;">My talk will discuss these problems and their connections. Here is an open problem that I would like to understand better: what is the maximum possible second eigenvalue multiplicity of a connected bounded degree graph?</p>
<p style="margin: 10px 0;padding: 0;mso-line-height-rule: exactly;-ms-text-size-adjust: 100%;-webkit-text-size-adjust: 100%;color: #757575;font-family: Helvetica;font-size: 16px;line-height: 150%;text-align: left;">Joint work with Zilin Jiang, Jonathan Tidor, Yuan Yao, and Shengtong Zhang</p>
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<p style="margin: 10px 0;padding: 0;mso-line-height-rule: exactly;-ms-text-size-adjust: 100%;-webkit-text-size-adjust: 100%;color: #757575;font-family: Helvetica;font-size: 16px;line-height: 150%;text-align: left;"><strong>Time: </strong>Mar 30, 2022 03:00 PM Central Time (US and Canada)</p>
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