<div dir="ltr"><div><div class="gmail_default" style="font-family:georgia,serif;font-size:small;color:rgb(0,0,0)"><b>When:         </b>October 24th <b>at <span style="background-color:rgb(255,255,0)">11am CT  </span></b></div><div><div class="gmail_default"><div dir="ltr"><p class="MsoNormal" style="margin:0in;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font color="#000000" face="georgia, serif"> <br><b>Where:</b><b>  </b>      Talk will be given<span style="background-color:rgb(255,255,0)"> </span><span style="background-color:rgb(255,255,0)"><font style="font-weight:bold"><u>live, in-person</u></font><font style="font-weight:bold"> </font></span>at</font></p><p class="MsoNormal" style="margin:0in;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font color="#000000" face="georgia, serif">                       TTIC, 6045 S. Kenwood Avenue</font></p><p class="MsoNormal" style="margin:0in;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font color="#000000" face="georgia, serif">                        5th Floor, Room 530<b>              </b>   </font></p><p class="MsoNormal" style="margin:0in;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font color="#000000" face="georgia, serif"><br></font></p><p class="MsoNormal" style="margin:0in;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="georgia, serif" color="#000000"><b><span class="gmail_default"></span>Virtually:</b>    via Panopto (<a href="https://uchicago.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=fa51bcae-403d-4e1d-b1c8-b31a00f2af6d" target="_blank">Livestream</a>) </font></p><font face="georgia, serif"><font color="#000000"> <br><b>Who:</b>            Jeff Xu, TTIC<br><br><b>Title:</b>            </font>Smooth Tradeoff for Tensor PCA via Sharp Matrix Bounds</font></div><div dir="ltr"><font face="georgia, serif"><br></font></div><div dir="ltr"><font face="georgia, serif"><b>Abstract: </b>     Tensor Principle Component Analysis (PCA) is a canonical problem in high-dimensional statistical inferences. Prior works have shown the success of various spectral algorithms essentially matching the conjectured computational thresholds for this problem, and it is known that (at least) in the sub-exponential time regime, similar to random CSP refutation, Tensor PCA exhibits a smooth tradeoff in signal-strength and runtime: increasing run-time allows one to detect a weaker signal. However, it is not clear whether such tradeoff appears in the polynomial-time regime, and establishing such a trade-off has crucial implications for quantum speed-ups.  Recently, the work of Bandeira et al. makes partial progress by establishing a smooth trade-off in a “limited" polytime regime via techniques from free probability.  In this talk, I will sketch a self-contained combinatorial argument for resolving this conjecture in its full generality, and highlight some open question along this direction.<br><br>Based on a joint work with Pravesh K. Kothari that can be found in <a href="https://arxiv.org/abs/2510.03061" target="_blank">https://arxiv.org/abs/2510.03061</a>.</font><br><p class="MsoNormal" style="margin:0in;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="georgia, serif" color="#000000"><br></font></p><p class="MsoNormal" style="margin:0in;font-family:georgia,serif;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="georgia, serif" color="#000000"><br></font></p></div></div><div style="font-family:georgia,serif"><div class="gmail_default"><b><font color="#000000" face="georgia, serif">*********************************************************************************************</font></b></div><p class="MsoNormal" style="margin:0in 0in 8pt;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial;line-height:15.6933px"><b><i><font color="#000000" face="georgia, serif">Research at TTIC Seminar Series</font></i></b></p><p class="MsoNormal" style="margin:0in;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font color="#000000" face="georgia, serif"> </font></p><div class="gmail_default"><div dir="ltr"><div class="gmail_default"><div dir="ltr"><p class="MsoNormal" style="margin:0in;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="georgia, serif" color="#000000">TTIC is hosting a weekly seminar series presenting the research currently underway at the Institute. Every week a different TTIC faculty member will present their research.  The lectures are intended for students seeking research topics and advisors, and for the general TTIC and University of Chicago communities interested in hearing what their colleagues are up to.</font></p><p class="MsoNormal" style="margin:0in;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="georgia, serif" color="#000000"><br></font></p><p class="MsoNormal" style="margin:0in;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="georgia, serif" color="#000000"><br></font></p></div></div></div></div></div></div><br clear="all"></div><div><div dir="ltr" class="gmail_signature" data-smartmail="gmail_signature"><div dir="ltr"><b style="background-color:rgb(255,255,255)"><font color="#3d85c6">Brandie Jones </font></b><div><div><div><font color="#3d85c6"><b><i>Executive </i></b></font><b style="color:rgb(61,133,198)"><i>Administrative Assistant</i></b></div></div><div><b style="color:rgb(61,133,198)"><i>Outreach Administrator </i></b></div><div><span style="background-color:rgb(255,255,255)"><font color="#3d85c6">Toyota Technological Institute</font></span></div><div><span style="background-color:rgb(255,255,255)"><font color="#3d85c6">6045 S. Kenwood Avenue</font></span></div><div><span style="background-color:rgb(255,255,255)"><font color="#3d85c6">Chicago, IL  60637</font></span></div></div><div><span style="background-color:rgb(255,255,255)"><font color="#3d85c6"><a href="http://www.ttic.edu" target="_blank">www.ttic.edu</a> </font></span></div><div><span style="background-color:rgb(255,255,255)"><font color="#3d85c6"><br></font></span></div></div></div></div></div>