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<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;color:#212121">This is an announcement of Tushant Mittal<span class="outlook-search-highlight">’s Candidacy</span><span class="apple-converted-space"> </span><span class="outlook-search-highlight">Exam</span>.
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Candidate: Tushant Mittal<br>
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Date: May 3, 2024.<br>
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Time: 3 PM.<br>
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Location: TTIC 529, Fifth Floor<br>
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Remote location:<span class="apple-converted-space"> </span></span><span style="font-family:"Arial",sans-serif"><a href="https://urldefense.com/v3/__https:/uchicago.zoom.us/j/99961926847?pwd=V1lTY1lQTk9xV2QyTDROS1F2V1VPZz09__;!!BpyFHLRN4TMTrA!7MsNkC6oS1tvwx24WRwpmiKA3lr72GwJITf1Y60lcjdw5ZDQnENi6HFqzcbJ_v7NPZHU6Irht5J8jZHxCsWNEic$" target="_blank" title="https://urldefense.com/v3/__https://uchicago.zoom.us/j/99961926847?pwd=V1lTY1lQTk9xV2QyTDROS1F2V1VPZz09__;!!BpyFHLRN4TMTrA!7MsNkC6oS1tvwx24WRwpmiKA3lr72GwJITf1Y60lcjdw5ZDQnENi6HFqzcbJ_v7NPZHU6Irht5J8jZHxCsWNEic$"><span style="color:#0078D7">https://uchicago.zoom.us/j/99961926847?pwd=V1lTY1lQTk9xV2QyTDROS1F2V1VPZz09</span></a><span class="apple-converted-space"><span style="color:#212121"> <o:p></o:p></span></span></span></p>
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<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;color:#212121">Meeting ID: 999 6192 6847 Passcode: 146080<br>
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Title: Expanders with Abelian symmetries and Quantum LDPC Codes<span class="apple-converted-space"> </span><br>
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Abstract: <span class="apple-converted-space"> </span><br>
One method to construct expander graphs with abelian symmetries is via the technique of graph lifts introduced by Bilu and Linial. For an abelian group G acting on the set [</span><span style="font-family:"Cambria Math",serif;color:#212121">𝓁</span><span style="font-family:"Arial",sans-serif;color:#212121">],
an (G,</span><span style="font-family:"Cambria Math",serif;color:#212121">𝓁</span><span style="font-family:"Arial",sans-serif;color:#212121">)-lift of a graph X is a graph obtained by replacing each vertex by
</span><span style="font-family:"Cambria Math",serif;color:#212121">𝓁</span><span style="font-family:"Arial",sans-serif;color:#212121"> copies, and each edge by a matching corresponding to the action of an element of G.<span class="apple-converted-space"> </span><br>
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In this talk, we will see how to analyze the expansion of lifted graphs and give explicit constructions of expanders via this approach. As a corollary, we obtain explicit quantum lifted product codes with almost linear distance and explicit classical quasi-cyclic
LDPC codes with a wide range of circulant sizes.<span class="apple-converted-space"> </span><br>
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This is based on joint work with Fernando Granha Jeronimo, Ryan O'Donnell, Pedro Paredes, and Madhur Tulsiani.<br>
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Advisors: Janos Simon, Madhur Tulsiani<br style="caret-color: rgb(33, 33, 33);font-variant-caps: normal;orphans: auto;text-align:start;widows: auto;-webkit-text-stroke-width: 0px;word-spacing:0px">
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<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;color:#212121">Committee: Janos Simon, Madhur Tulsiani, Ryan O'Donnell, and Bill Fefferman.</span><span style="font-family:"Arial",sans-serif"><o:p></o:p></span></p>
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