<html><head><meta http-equiv="content-type" content="text/html; charset=utf-8"></head><body dir="auto"><div class="WordSection1" style="-webkit-text-size-adjust: auto; page: WordSection1;"><p class="MsoNormal" style="margin: 0in; font-size: 10pt; font-family: Calibri, sans-serif;"><b><span style="font-size: 12pt; font-family: Helvetica;">Aravindan Vijayaraghaven</span></b><o:p></o:p></p><p class="MsoNormal" style="margin: 0in; font-size: 10pt; font-family: Calibri, sans-serif;"><b><span style="font-size: 11pt; font-family: Helvetica;">Northwestern University</span></b><o:p></o:p></p><p class="MsoNormal" style="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="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="margin: 0in; font-size: 10pt; font-family: Calibri, sans-serif;"><img width="250" height="250" id="Picture_x0020_3" src="cid:A8C88639-A316-4C0D-8461-2FEA7BDA866A" _mf_state="1" title="null" alt="image001.jpg" style="width: 2.6041in; height: 2.6041in;"><o:p></o:p></p><p class="MsoNormal" style="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="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="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">February 14</span><span dir="ltr">, 202</span><span dir="ltr">3</span><span dir="ltr"> at 3:30pm</span></span></b><o:p></o:p></p><p class="MsoNormal" style="margin: 0in; font-size: 10pt; font-family: Calibri, sans-serif;"><b><span style="font-size: 11pt; background-color: yellow;">Kent Chemical Laboratory, Room 102</span></b><o:p></o:p></p><p class="MsoNormal" style="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="margin: 0in; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></p><p style="margin: 0in;"><b><i><span style="font-size: 12pt;">Title:</span></i></b><span style="font-size: 12pt;"> Computing linear sections of varieties: quantum entanglement, tensor</span><span style="font-size: 10pt; font-family: "Helvetica Neue";"></span><span style="font-size: 12pt;">decompositions and beyond</span><o:p></o:p></p><p class="MsoNormal" style="margin: 0in; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></p><p style="margin: 0in;"><b><i><span style="font-size: 12pt;">Abstract:</span></i></b><b><span style="font-size: 12pt;"> </span></b><span style="font-size: 12pt;"> Abstract: We study the problem of finding elements in the intersection of an arbitrary conic variety (over reals or complex numbers) with a given linear subspace. This problem captures a rich family of algorithmic problems under different choices of the variety. The special case of the variety consisting of rank-1 matrices already has strong connections to central problems in different areas like quantum information theory and tensor decompositions.<span class="apple-converted-space"> </span><br> Despite the worst-case NP-hardness of this problem, we give efficient algorithms that solve this problem for "typical" subspaces i.e., those chosen generically of a certain dimension, potentially with some generic elements of the variety contained in it, under some mild non-degeneracy assumptions on the variety. These also imply new algorithmic results for low-rank decomposition problems that go beyond tensor decompositions, and problems in quantum entanglement.<br> </span></p><p style="margin: 0in;"><span style="font-size: 12pt;">This is based on joint work with Nathaniel Johnston and Benjamin Lovitz.<span class="apple-converted-space"> </span></span><o:p></o:p></p><p> <o:p></o:p></p><p><b><i><span style="font-size: 12pt;">Bio:</span></i></b><span style="font-size: 12pt;"> <span style="background-color: white;">I’m an </span><span style="color: rgb(52, 47, 46); background-color: white;">Associate Professor of Computer Science and Industrial Engineering & Management Sciences at Northwestern University in Evanston, IL</span><span style="background-color: white;">. I received my PhD in Computer Science from Princeton University.</span></span><o:p></o:p></p><p> <o:p></o:p></p><p style="margin-bottom: 12pt;"><br></p></div><div dir="ltr"></div></body></html>