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<p class="MsoNormal"><i><span style="font-size:12.0pt;font-family:Helvetica;color:#8B0102"> </span></i><o:p></o:p></p>
<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">Siqi Liu, PhD</span></b><o:p></o:p></p>
<p class="MsoNormal"><b><span style="font-size:11.0pt;font-family:Helvetica">University of California, Berkeley</span></b><o:p></o:p></p>
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<p class="MsoNormal"><b><span style="font-size:11.0pt;font-family:Helvetica;color:black"> </span></b><b><span style="font-size:11.0pt;color:black">Tuesday,
</span></b><b><span style="font-size:11.0pt">November 12<span style="color:black">, 202</span>4<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 class="MsoNormal"><b><i><span style="font-size:12.0pt">Title: </span></i></b><span style="font-size:12.0pt">Sparse spectral and coboundary high dimensional expanders<b><i><o:p></o:p></i></b></span></p>
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<p class="MsoNormal"><b><i><span style="font-size:12.0pt">Abstract</span></i></b><span style="font-size:12.0pt">: High dimensional expanders (HDXs) are a class of expanding hypergraphs. Their importance is constantly growing with their roles in the breakthroughs
in Markov chains [ALGV19], locally testable codes [DELLM22], and quantum codes [PP22, ABN23]. HDXs generalize the notion of expander graphs but differ from the latter in a couple ways. First, while various definitions of expansion are equivalent over graphs,
they are different in hypergraphs, yielding different types of HDXs. Secondly, while sparse expanders are abundant in random graph models, bounded-degree HDXs seem to be rare in random hypergraph models. <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt">So far, the sparest random construction of HDXs comes from random geometric graphs (RGGs) [LMSY23]. In this talk we will introduce a deterministic construction of HDXs which can be viewed as a derandomization
of the RGG construction. These hypergraphs are both spectral HDXs and coboundary HDXs. They are the sparsest known coboundary HDXs (over any group). In particular, their 1-skeletons are abelian Cayley graphs.<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt">This is based on joint work with Yotam Dikstein and Avi Wigderson.<o:p></o:p></span></p>
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<p class="MsoNormal"><b><i><span style="font-size:12.0pt">Bio:</span></i></b><span style="font-size:12.0pt"> I am a postdoc at the Institute for Advanced Study. I got my PhD in Computer Science from UC Berkeley in 2023, advised by Alessandro Chiesa. I am interested
in constructing expanding graphs and hypergraphs and applying them to build codes and proof systems.<o:p></o:p></span></p>
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<p style="margin-bottom:12.0pt"><b><span style="font-family:Helvetica;color:black">Host:<span class="apple-converted-space"> Aaron Potechin</span></span></b><br>
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