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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">Srikanth Srinivasan</span></b><o:p></o:p></p>
<p class="MsoNormal"><b><span style="font-size:11.0pt;font-family:Helvetica">Aarhus University, Aarhus, Denmark</span></b><o:p></o:p></p>
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<p class="MsoNormal"><img width="217" height="290" style="width:2.2604in;height:3.0208in" id="Picture_x0020_3" src="cid:image001.jpg@01D93A18.161EE590" alt="srikanth Srinivasan"><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 21<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">
<span style="color:#212121">Lower Bounds for Set-Multilinear Algebraic Formulas</span></span><o:p></o:p></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:#212121">Say we have a multivariate polynomial P(x_1,..., x_n). An Algebraic formula for P is just an algebraic expression for P with nested additions and multiplications. A small formula for P implies
an efficient algorithm for evaluating P, and so a lower bound on the size of any such expression implies that P is possibly hard to evaluate.<br>
<span class="apple-converted-space"> </span><br>
How would you show that your favorite polynomial P has no small formula? In this talk, we will see a technique (building on works of Nisan, Wigderson and Raz) for doing this that combines some linear algebra with random restrictions, which are a classical tool
in circuit complexity. This helps us prove lower bounds for special kinds of algebraic formulas, called set-multilinear formulas.<br>
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<p style="margin:0in"><span style="font-size:12.0pt;color:#212121">Based on joint work with Nutan Limaye (ITU) and Sébastien Tavenas (USMB, Univ Grenoble). The paper can be found at:
</span><a href="https://urldefense.com/v3/__https:/eccc.weizmann.ac.il/report/2021/094/__;!!BpyFHLRN4TMTrA!_jvh72boR_G5MShz_-df-YHKy6ZC_4Ix4MKW3SmM2EftKbfGSUk7mmQp204YbXhtxk6Ye22MkRXZ98i-wqIT_HxuEw$"><span style="font-size:12.0pt">https://eccc.weizmann.ac.il/report/2021/094/</span></a><span class="apple-converted-space"><span style="font-size:12.0pt;color:#212121"> </span></span><o:p></o:p></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 at Aarhus University in Aarhus, Denmark</span><span style="color:black;background:white">. I received my PhD from
The Institute of Mathematical Sciences, in Tamil Nadu, India.</span></span><o:p></o:p></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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