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<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
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<p class="MsoNormal"><i><span style="font-size:12.0pt;font-family:Helvetica;color:#8B0102">UNIVERSITY OF CHICAGO</span></i><o:p></o:p></p>
<p class="MsoNormal"><i><span style="font-size:12.0pt;font-family:Helvetica;color:#8B0102">COMPUTER SCIENCE DEPARTMENT</span></i><o:p></o:p></p>
<p class="MsoNormal"><i><span style="font-size:12.0pt;font-family:Helvetica;color:#8B0102">PRESENTS</span></i><o:p></o:p></p>
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<p class="MsoNormal"><b><span style="font-size:12.0pt;font-family:Helvetica">Aravindan Vijayaraghaven</span></b><o:p></o:p></p>
<p class="MsoNormal"><b><span style="font-size:11.0pt;font-family:Helvetica">Northwestern University</span></b><o:p></o:p></p>
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<p class="MsoNormal"><img width="250" height="250" style="width:2.6041in;height:2.6041in" id="Picture_x0020_3" src="cid:image001.jpg@01D936F1.E9B87B20"><o:p></o:p></p>
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<p class="MsoNormal"><b><span style="font-size:11.0pt;color:black">Tuesday, </span>
</b><b><span style="font-size:11.0pt">February 14<span style="color:black">, 202</span>3<span style="color:black"> at 3:30pm</span></span></b><o:p></o:p></p>
<p class="MsoNormal"><b><span style="font-size:11.0pt;color:black;background:yellow">Kent Chemical Laboratory, Room 102</span></b><o:p></o:p></p>
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<p style="margin:0in"><b><i><span style="font-size:12.0pt">Title:</span></i></b><span style="font-size:12.0pt"> Computing linear sections of varieties: quantum entanglement, tensor</span><span style="font-size:10.0pt;font-family:"Helvetica Neue";color:black">
</span><span style="font-size:12.0pt;color:black">decompositions and beyond</span></p>
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<p style="margin:0in"><b><i><span style="font-size:12.0pt">Abstract:</span></i></b><b><span style="font-size:12.0pt">
</span></b><span style="font-size:12.0pt"> <span style="color:black">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>
><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 class="apple-converted-space"> </span><br>
> This is based on joint work with Nathaniel Johnston and Benjamin Lovitz.<span class="apple-converted-space"> </span></span></span><span style="font-size:12.0pt"><o:p></o:p></span></p>
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<p><b><i><span style="font-size:12.0pt">Bio:</span></i></b><span style="font-size:12.0pt">
<span style="color:black;background:white">I’m an </span><span style="color:#342F2E;background:white">Associate Professor of Computer Science and Industrial Engineering & Management Sciences at Northwestern University in Evanston, IL</span><span style="color:black;background:white">.
I received my PhD in Computer Science from Princeton University.</span></span></p>
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<p style="margin-bottom:12.0pt"><b><span style="font-size:12.0pt;font-family:Helvetica;color:black">Host:<span class="apple-converted-space"> Alexander Razborov</span></span></b><br>
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