<html><head><meta http-equiv="content-type" content="text/html; charset=us-ascii"></head><body dir="auto"><p class="MsoNormal" style="-webkit-text-size-adjust: auto; margin: 0in; font-size: 10pt; font-family: Calibri, sans-serif;"><b><span style="font-size: 12pt; font-family: Helvetica;">Haotian Jiang, PhD</span></b><o:p></o:p></p><p class="MsoNormal" style="-webkit-text-size-adjust: auto; margin: 0in; font-size: 10pt; font-family: Calibri, sans-serif;"><b><span style="font-size: 11pt; font-family: Helvetica;">Assistant Professor, University of Chicago</span></b><o:p></o:p></p><p class="MsoNormal" style="-webkit-text-size-adjust: auto; margin: 0in; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></p><p class="MsoNormal" style="-webkit-text-size-adjust: auto; margin: 0in; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></p><p class="MsoNormal" style="-webkit-text-size-adjust: auto; margin: 0in; font-size: 10pt; font-family: Calibri, sans-serif;"><img width="240" height="244" id="Picture_x0020_2" src="cid:8EDAB4F7-7D49-4E3D-AB4A-F96C05A1F561" _mf_state="1" title="null" alt="image001.png" style="width: 2.5in; height: 2.5416in;"><o:p></o:p></p><p class="MsoNormal" style="-webkit-text-size-adjust: auto; margin: 0in; font-size: 10pt; font-family: Calibri, sans-serif;"><b><span style="font-size: 11pt; font-family: Helvetica;"> </span></b><o:p></o:p></p><p class="MsoNormal" style="-webkit-text-size-adjust: auto; margin: 0in; font-size: 10pt; font-family: Calibri, sans-serif;"><b><span style="font-size: 11pt; font-family: Helvetica;"> </span></b><o:p></o:p></p><p class="MsoNormal" style="-webkit-text-size-adjust: auto; margin: 0in; font-size: 10pt; font-family: Calibri, sans-serif;"><b><span style="font-size: 11pt;"><span dir="ltr">Tuesday, </span></span></b><b><span style="font-size: 11pt;"><span dir="ltr">October 1</span><span dir="ltr">, 202</span><span dir="ltr">4</span><span dir="ltr"> at 3:30pm</span></span></b><o:p></o:p></p><p class="MsoNormal" style="-webkit-text-size-adjust: auto; margin: 0in; font-size: 10pt; font-family: Calibri, sans-serif;"><b><span style="font-size: 11pt; background: yellow;">Location: Kent 102</span></b><o:p></o:p></p><p class="MsoNormal" style="-webkit-text-size-adjust: auto; margin: 0in; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></p><p class="MsoNormal" style="-webkit-text-size-adjust: auto; margin: 0in; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><b><i><u><span style="font-size: 14pt;">Title:</span></u></i></b><i><span style="font-size: 14pt;"> </span></i><span style="font-size: 12pt;">Tensor Concentration Inequalities: A Geometric Approach</span><o:p></o:p></p><p class="MsoNormal" style="-webkit-text-size-adjust: auto; margin: 0in; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></p><p class="MsoNormal" style="-webkit-text-size-adjust: auto; margin: 0in; font-size: 10pt; font-family: Calibri, sans-serif;"><b><i><u><span style="font-size: 14pt;">Abstract:</span></u></i></b><span style="font-size: 11pt;"> </span><span style="font-size: 12pt;">Matrix Concentration inequalities, commonly used in the forms of Matrix Chernoff Bounds or the Non-Commutative Khintchine Inequality, are central to a wide range of applications in computer science and mathematics. However, they fall short in many applications where tensor versions of these inequalities are required. </span><o:p></o:p></p><p class="MsoNormal" style="-webkit-text-size-adjust: auto; margin: 0in; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 12pt;"> </span><o:p></o:p></p><p class="MsoNormal" style="-webkit-text-size-adjust: auto; margin: 0in; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 12pt;">In this work, we study concentration inequalities for the $\ell_p$-injective norms of sums of independent tensors. We obtain the first such inequalities beyond Rudelson's classical work on rank-1 tensors, and our tensor concentration inequalities are tight in certain regimes of $p$ and the order of the tensors. Our results are obtained via a geometric argument based on estimating the covering numbers for the natural stochastic processes corresponding to tensor injective norms. </span><o:p></o:p></p><p class="MsoNormal" style="-webkit-text-size-adjust: auto; margin: 0in; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 12pt;"> </span><o:p></o:p></p><p class="MsoNormal" style="-webkit-text-size-adjust: auto; margin: 0in; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 12pt;">We also discuss applications and connections of our inequalities to various other problems, e.g. tensor PCA, locally-decodable codes, and natural models for random tensors and their tensor extensions. </span></p><div dir="ltr"></div></body></html>