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Henry Cohn - Wikipedia

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</div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">American mathematician</div> <style data-mw-deduplicate="TemplateStyles:r1257001546">.mw-parser-output .infobox-subbox{padding:0;border:none;margin:-3px;width:auto;min-width:100%;font-size:100%;clear:none;float:none;background-color:transparent}.mw-parser-output .infobox-3cols-child{margin:auto}.mw-parser-output .infobox .navbar{font-size:100%}@media screen{html.skin-theme-clientpref-night .mw-parser-output .infobox-full-data:not(.notheme)>div:not(.notheme)[style]{background:#1f1f23!important;color:#f8f9fa}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .infobox-full-data:not(.notheme) div:not(.notheme){background:#1f1f23!important;color:#f8f9fa}}@media(min-width:640px){body.skin--responsive .mw-parser-output .infobox-table{display:table!important}body.skin--responsive .mw-parser-output .infobox-table>caption{display:table-caption!important}body.skin--responsive .mw-parser-output .infobox-table>tbody{display:table-row-group}body.skin--responsive .mw-parser-output .infobox-table tr{display:table-row!important}body.skin--responsive .mw-parser-output .infobox-table th,body.skin--responsive .mw-parser-output .infobox-table td{padding-left:inherit;padding-right:inherit}}</style><table class="infobox biography vcard"><tbody><tr><th colspan="2" class="infobox-above" style="font-size:125%;"><div class="fn">Henry Cohn</div></th></tr><tr><td colspan="2" class="infobox-image"><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/File:Henry_Cohn.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Henry_Cohn.jpg/220px-Henry_Cohn.jpg" decoding="async" width="220" height="146" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Henry_Cohn.jpg/330px-Henry_Cohn.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/7/7b/Henry_Cohn.jpg 2x" data-file-width="400" data-file-height="266" /></a></span><div class="infobox-caption">Henry Cohn at <a href="/wiki/Mathematical_Research_Institute_of_Oberwolfach" class="mw-redirect" title="Mathematical Research Institute of Oberwolfach">Oberwolfach</a>, June 2014<br />Photo by Ivonne Vetter</div></td></tr><tr><th scope="row" class="infobox-label">Alma&#160;mater</th><td class="infobox-data"><a href="/wiki/Massachusetts_Institute_of_Technology" title="Massachusetts Institute of Technology">MIT</a><sup id="cite_ref-website_2-0" class="reference"><a href="#cite_note-website-2"><span class="cite-bracket">&#91;</span>2<span class="cite-bracket">&#93;</span></a></sup><br /><a href="/wiki/Harvard_University" title="Harvard University">Harvard</a></td></tr><tr><th scope="row" class="infobox-label">Known&#160;for</th><td class="infobox-data"><a href="/wiki/Sphere_packing" title="Sphere packing">Sphere packing</a></td></tr><tr><td colspan="2" class="infobox-full-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1257001546"><b>Scientific career</b></td></tr><tr><th scope="row" class="infobox-label">Fields</th><td class="infobox-data category">Mathematics</td></tr><tr><th scope="row" class="infobox-label">Institutions</th><td class="infobox-data"><a href="/wiki/Microsoft_Research" title="Microsoft Research">Microsoft Research</a></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Thesis" title="Thesis">Thesis</a></th><td class="infobox-data"><i> New Bounds on Sphere Packings </i>&#160;<span style="font-size:97%;">(2000)</span></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Doctoral_advisor" title="Doctoral advisor">Doctoral advisor</a></th><td class="infobox-data"><a href="/wiki/Noam_Elkies" title="Noam Elkies">Noam Elkies</a><sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">&#91;</span>1<span class="cite-bracket">&#93;</span></a></sup></td></tr><tr style="display:none"><td colspan="2"> </td></tr><tr><th scope="row" class="infobox-label">Website</th><td class="infobox-data"><a rel="nofollow" class="external free" href="https://cohn.mit.edu/">https://cohn.mit.edu/</a></td></tr></tbody></table> <p><b>Henry Cohn</b> is an American mathematician. He is a principal researcher at <a href="/wiki/Microsoft_Research" title="Microsoft Research">Microsoft Research</a> and an adjunct professor at <a href="/wiki/Massachusetts_Institute_of_Technology" title="Massachusetts Institute of Technology">MIT</a>.<sup id="cite_ref-website_2-1" class="reference"><a href="#cite_note-website-2"><span class="cite-bracket">&#91;</span>2<span class="cite-bracket">&#93;</span></a></sup> In collaboration with Abhinav Kumar, Stephen D. Miller, Danylo Radchenko, and <a href="/wiki/Maryna_Viazovska" title="Maryna Viazovska">Maryna Viazovska</a>, he solved the <a href="/wiki/Sphere_packing" title="Sphere packing">sphere packing</a> problem in 24 dimensions.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">&#91;</span>3<span class="cite-bracket">&#93;</span></a></sup> In 2003, with <a href="/wiki/Chris_Umans" title="Chris Umans">Chris Umans</a> he initiated a group-theoretic approach to matrix multiplication,<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">&#91;</span>4<span class="cite-bracket">&#93;</span></a></sup> and is a core contributor to its continued development with various coauthors.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">&#91;</span>5<span class="cite-bracket">&#93;</span></a></sup><sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">&#91;</span>6<span class="cite-bracket">&#93;</span></a></sup><sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">&#91;</span>7<span class="cite-bracket">&#93;</span></a></sup><sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">&#91;</span>8<span class="cite-bracket">&#93;</span></a></sup><sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">&#91;</span>9<span class="cite-bracket">&#93;</span></a></sup> </p><p>Cohn graduated from <a href="/wiki/Harvard_University" title="Harvard University">Harvard University</a> in 2000 with a doctorate in mathematics.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">&#91;</span>10<span class="cite-bracket">&#93;</span></a></sup> Cohn was an <a href="/wiki/Erd%C5%91s_Lectures" title="Erdős Lectures">Erdős Lecturer</a> at <a href="/wiki/Hebrew_University_of_Jerusalem" title="Hebrew University of Jerusalem">Hebrew University of Jerusalem</a> in 2008. In 2016, he became a <a href="/wiki/Learned_society_fellow" class="mw-redirect" title="Learned society fellow">Fellow</a> of the <a href="/wiki/American_Mathematical_Society" title="American Mathematical Society">American Mathematical Society</a> "for contributions to discrete mathematics, including applications to computer science and physics."<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">&#91;</span>11<span class="cite-bracket">&#93;</span></a></sup> </p><p>In 2018, he was awarded the <a href="/wiki/Levi_L._Conant_Prize" title="Levi L. Conant Prize">Levi L. Conant Prize</a> for his article “A Conceptual Breakthrough in Sphere Packing,” published in 2017 in the <i><a href="/wiki/Notices_of_the_AMS" class="mw-redirect" title="Notices of the AMS">Notices of the AMS</a></i>.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">&#91;</span>12<span class="cite-bracket">&#93;</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Henry_Cohn&amp;action=edit&amp;section=1" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://mathgenealogy.org/id.php?id=47141">Henry Cohn</a> at the <a href="/wiki/Mathematics_Genealogy_Project" title="Mathematics Genealogy Project">Mathematics Genealogy Project</a></span> </li> <li id="cite_note-website-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-website_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-website_2-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://math.mit.edu/~cohn/">"Henry Cohn"</a><span class="reference-accessdate">. Retrieved <span class="nowrap">14 July</span> 2017</span>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&amp;rft.genre=unknown&amp;rft.btitle=Henry+Cohn&amp;rft_id=http%3A%2F%2Fmath.mit.edu%2F~cohn%2F&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenry+Cohn" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKlarreich2016" class="citation web cs1"><a href="/wiki/Erica_Klarreich" title="Erica Klarreich">Klarreich, Erica</a> (30 March 2016). <a rel="nofollow" class="external text" href="https://www.quantamagazine.org/sphere-packing-solved-in-higher-dimensions-20160330/">"Sphere Packing Solved in Higher Dimensions"</a>. <i><a href="/wiki/Quanta_Magazine" title="Quanta Magazine">Quanta Magazine</a></i><span class="reference-accessdate">. Retrieved <span class="nowrap">14 July</span> 2017</span>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=unknown&amp;rft.jtitle=Quanta+Magazine&amp;rft.atitle=Sphere+Packing+Solved+in+Higher+Dimensions&amp;rft.date=2016-03-30&amp;rft.aulast=Klarreich&amp;rft.aufirst=Erica&amp;rft_id=https%3A%2F%2Fwww.quantamagazine.org%2Fsphere-packing-solved-in-higher-dimensions-20160330%2F&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenry+Cohn" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCohnUmans2003" class="citation conference cs1">Cohn, Henry; Umans, Christopher (2003). <a rel="nofollow" class="external text" href="https://doi.org/10.1109/SFCS.2003.1238217">"A group-theoretic approach to fast matrix multiplication"</a>. <i>Proc. 44th Annual IEEE Symposium on Foundations of Computer Science (FOCS)</i>. IEEE. pp.&#160;438–449. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/math/0307321">math/0307321</a></span>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FSFCS.2003.1238217">10.1109/SFCS.2003.1238217</a>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&amp;rft.genre=conference&amp;rft.atitle=A+group-theoretic+approach+to+fast+matrix+multiplication&amp;rft.btitle=Proc.+44th+Annual+IEEE+Symposium+on+Foundations+of+Computer+Science+%28FOCS%29&amp;rft.pages=438-449&amp;rft.pub=IEEE&amp;rft.date=2003&amp;rft_id=info%3Aarxiv%2Fmath%2F0307321&amp;rft_id=info%3Adoi%2F10.1109%2FSFCS.2003.1238217&amp;rft.aulast=Cohn&amp;rft.aufirst=Henry&amp;rft.au=Umans%2C+Christopher&amp;rft_id=https%3A%2F%2Fdoi.org%2F10.1109%2FSFCS.2003.1238217&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenry+Cohn" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCohnKleinbergSzegedyUmans2005" class="citation conference cs1">Cohn, Henry; Kleinberg, Robert; Szegedy, Balász; Umans, Christopher (2005). <a rel="nofollow" class="external text" href="https://doi.org/10.1109/SFCS.2005.39">"Group-theoretic Algorithms for Matrix Multiplication"</a>. <i>Proc. 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS)</i>. IEEE. pp.&#160;379–388. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/math/0511460">math/0511460</a></span>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FSFCS.2005.39">10.1109/SFCS.2005.39</a>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&amp;rft.genre=conference&amp;rft.atitle=Group-theoretic+Algorithms+for+Matrix+Multiplication&amp;rft.btitle=Proc.+46th+Annual+IEEE+Symposium+on+Foundations+of+Computer+Science+%28FOCS%29&amp;rft.pages=379-388&amp;rft.pub=IEEE&amp;rft.date=2005&amp;rft_id=info%3Aarxiv%2Fmath%2F0511460&amp;rft_id=info%3Adoi%2F10.1109%2FSFCS.2005.39&amp;rft.aulast=Cohn&amp;rft.aufirst=Henry&amp;rft.au=Kleinberg%2C+Robert&amp;rft.au=Szegedy%2C+Bal%C3%A1sz&amp;rft.au=Umans%2C+Christopher&amp;rft_id=https%3A%2F%2Fdoi.org%2F10.1109%2FSFCS.2005.39&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenry+Cohn" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCohnUmans2013" class="citation conference cs1">Cohn, Henry; Umans, Christopher (2013). <a rel="nofollow" class="external text" href="https://doi.org/10.1137/1.9781611973105.77">"Fast matrix multiplication using coherent configurations"</a>. <i>Proc. 24th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)</i>. SIAM. pp.&#160;1074–1087. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1207.6528">1207.6528</a></span>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1137%2F1.9781611973105.77">10.1137/1.9781611973105.77</a>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&amp;rft.genre=conference&amp;rft.atitle=Fast+matrix+multiplication+using+coherent+configurations&amp;rft.btitle=Proc.+24th+Annual+ACM-SIAM+Symposium+on+Discrete+Algorithms+%28SODA%29&amp;rft.pages=1074-1087&amp;rft.pub=SIAM&amp;rft.date=2013&amp;rft_id=info%3Aarxiv%2F1207.6528&amp;rft_id=info%3Adoi%2F10.1137%2F1.9781611973105.77&amp;rft.aulast=Cohn&amp;rft.aufirst=Henry&amp;rft.au=Umans%2C+Christopher&amp;rft_id=https%3A%2F%2Fdoi.org%2F10.1137%2F1.9781611973105.77&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenry+Cohn" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBlasiakChurchCohnGrochow2017" class="citation journal cs1">Blasiak, Jonah; Church, Thomas; Cohn, Henry; Grochow, Joshua A.; Naslund, Eric; Sawin, William F.; Umans, Christopher (2017). <a rel="nofollow" class="external text" href="https://doi.org/10.19086/da.1245">"On cap sets and the group-theoretic approach to matrix multiplication"</a>. <i>Discrete Analysis</i>. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1605.06702">1605.06702</a></span>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.19086%2Fda.1245">10.19086/da.1245</a>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=article&amp;rft.jtitle=Discrete+Analysis&amp;rft.atitle=On+cap+sets+and+the+group-theoretic+approach+to+matrix+multiplication&amp;rft.date=2017&amp;rft_id=info%3Aarxiv%2F1605.06702&amp;rft_id=info%3Adoi%2F10.19086%2Fda.1245&amp;rft.aulast=Blasiak&amp;rft.aufirst=Jonah&amp;rft.au=Church%2C+Thomas&amp;rft.au=Cohn%2C+Henry&amp;rft.au=Grochow%2C+Joshua+A.&amp;rft.au=Naslund%2C+Eric&amp;rft.au=Sawin%2C+William+F.&amp;rft.au=Umans%2C+Christopher&amp;rft_id=https%3A%2F%2Fdoi.org%2F10.19086%2Fda.1245&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenry+Cohn" class="Z3988"></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBlasiakChurchCohnGrochow2017" class="citation arxiv cs1">Blasiak, Jonah; Church, Thomas; Cohn, Henry; Grochow, Joshua A.; Umans, Christopher (2017). "Which groups are amenable to proving exponent two for matrix multiplication?". <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1712.02302">1712.02302</a></span> [<a rel="nofollow" class="external text" href="https://arxiv.org/archive/math.GR">math.GR</a>].</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=preprint&amp;rft.jtitle=arXiv&amp;rft.atitle=Which+groups+are+amenable+to+proving+exponent+two+for+matrix+multiplication%3F&amp;rft.date=2017&amp;rft_id=info%3Aarxiv%2F1712.02302&amp;rft.aulast=Blasiak&amp;rft.aufirst=Jonah&amp;rft.au=Church%2C+Thomas&amp;rft.au=Cohn%2C+Henry&amp;rft.au=Grochow%2C+Joshua+A.&amp;rft.au=Umans%2C+Christopher&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenry+Cohn" class="Z3988"></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBlasiakCohnGrochowPratt2023" class="citation conference cs1">Blasiak, Jonah; Cohn, Henry; Grochow, Joshua A.; Pratt, Kevin; Umans, Christopher (2023). "Matrix Multiplication via Matrix Groups". <i>14th Innovations in Theoretical Computer Science Conference (ITCS 2023)</i>. Schloss Dagstuhl - Leibniz-Zentrum für Informatik. pp.&#160;19:1–19:16. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.4230%2FLIPIcs.ITCS.2023.19">10.4230/LIPIcs.ITCS.2023.19</a></span>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&amp;rft.genre=conference&amp;rft.atitle=Matrix+Multiplication+via+Matrix+Groups&amp;rft.btitle=14th+Innovations+in+Theoretical+Computer+Science+Conference+%28ITCS+2023%29&amp;rft.pages=19%3A1-19%3A16&amp;rft.pub=Schloss+Dagstuhl+-+Leibniz-Zentrum+f%C3%BCr+Informatik&amp;rft.date=2023&amp;rft_id=info%3Adoi%2F10.4230%2FLIPIcs.ITCS.2023.19&amp;rft.aulast=Blasiak&amp;rft.aufirst=Jonah&amp;rft.au=Cohn%2C+Henry&amp;rft.au=Grochow%2C+Joshua+A.&amp;rft.au=Pratt%2C+Kevin&amp;rft.au=Umans%2C+Christopher&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenry+Cohn" class="Z3988"></span></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20220219165822/https://math.mit.edu/directory/profile.php?pid=1224">"Henry Cohn | MIT Mathematics"</a>. 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Retrieved <span class="nowrap">2017-12-22</span></span>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&amp;rft.genre=unknown&amp;rft.btitle=Henry+Cohn+%7C+MIT+Mathematics&amp;rft_id=http%3A%2F%2Fmath.mit.edu%2Fdirectory%2Fprofile.php%3Fpid%3D1224&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenry+Cohn" class="Z3988"></span></span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://www.ams.org/profession/fellows-list">List of Fellows of the American Mathematical Society</a>, retrieved 2017-08-09</span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.ams.org/journals/notices/201804/rnoti-p463.pdf">"2018 Levi L. Conant Prize"</a> <span class="cs1-format">(PDF)</span>. American Mathematical Society<span class="reference-accessdate">. Retrieved <span class="nowrap">7 September</span> 2018</span>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&amp;rft.genre=unknown&amp;rft.btitle=2018+Levi+L.+Conant+Prize&amp;rft.pub=American+Mathematical+Society&amp;rft_id=https%3A%2F%2Fwww.ams.org%2Fjournals%2Fnotices%2F201804%2Frnoti-p463.pdf&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenry+Cohn" class="Z3988"></span> </span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Henry_Cohn&amp;action=edit&amp;section=2" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKlarreich2019" class="citation web cs1"><a href="/wiki/Erica_Klarreich" title="Erica Klarreich">Klarreich, Erica</a> (2019-05-13). <a rel="nofollow" class="external text" href="https://www.quantamagazine.org/universal-math-solutions-in-dimensions-8-and-24-20190513/">"Out of a Magic Math Function, One Solution to Rule Them All"</a>. <i><a href="/wiki/Quanta_Magazine" title="Quanta Magazine">Quanta Magazine</a></i><span class="reference-accessdate">. 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style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bartok_(compiler)" title="Bartok (compiler)">Bartok</a></li> <li><a href="/wiki/Bosque_(programming_language)" title="Bosque (programming language)">Bosque</a></li> <li><a href="/wiki/C%CF%89" class="mw-redirect" title="Cω">Cω</a></li> <li><a href="/wiki/F*_(programming_language)" title="F* (programming language)">F*</a></li> <li><a href="/wiki/Lean_(proof_assistant)" title="Lean (proof assistant)">Lean</a></li> <li><a href="/wiki/P_(programming_language)" title="P (programming language)">P</a></li> <li><a href="/wiki/Project_Verona" title="Project Verona">Project Verona</a></li> <li><a href="/wiki/Microsoft_Phoenix" title="Microsoft Phoenix">Phoenix</a></li> <li><a href="/wiki/Polyphonic_C_Sharp" class="mw-redirect" title="Polyphonic C Sharp">Polyphonic C#</a></li> <li><a href="/wiki/SecPAL" title="SecPAL">SecPAL</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Distributed_computing" title="Distributed computing">Distributed</a>–<a href="/wiki/Grid_computing" title="Grid computing">grid computing</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/BitVault" title="BitVault">BitVault</a></li> <li><a href="/wiki/Confidential_Consortium_Framework" title="Confidential Consortium Framework">Confidential Consortium Framework</a></li> <li><a href="/wiki/DeepSpeed" title="DeepSpeed">DeepSpeed</a></li> <li><a href="/wiki/Orleans_(software_framework)" title="Orleans (software framework)">Orleans</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Internet" title="Internet">Internet</a>, <a href="/wiki/Computer_network" title="Computer network">networking</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/AjaxView" title="AjaxView">AjaxView</a></li> <li><a href="/wiki/Avalanche_(P2P)" title="Avalanche (P2P)">Avalanche</a></li> <li><a href="/wiki/Conference_XP" title="Conference XP">Conference XP</a></li> <li><a href="/wiki/Gazelle_(web_browser)" title="Gazelle (web browser)">Gazelle</a></li> <li><a href="/wiki/HoneyMonkey" title="HoneyMonkey">HoneyMonkey</a></li> <li><a href="/wiki/Penny_Black_(research_project)" title="Penny Black (research project)">Penny Black</a></li> <li><a href="/wiki/Wallop" title="Wallop">Wallop</a></li> <li><a href="/wiki/WikiBhasha" title="WikiBhasha">WikiBhasha</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other projects</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Microsoft_Automatic_Graph_Layout" title="Microsoft Automatic Graph Layout">Automatic Graph Layout</a></li> <li><a href="/wiki/Microsoft_Cognitive_Toolkit" title="Microsoft Cognitive Toolkit">Cognitive Toolkit</a></li> <li><a href="/wiki/Project_Digits" title="Project Digits">Digits</a></li> <li><a href="/wiki/Microsoft_Holoportation" title="Microsoft Holoportation">Holoportation</a></li> <li><a href="/wiki/IllumiRoom" title="IllumiRoom">IllumiRoom</a></li> <li><a href="/wiki/Image_Composite_Editor" title="Image Composite Editor">Image Composite Editor</a></li> <li><a href="/wiki/Infer.NET" title="Infer.NET">Infer.NET</a></li> <li><a href="/wiki/LightGBM" title="LightGBM">LightGBM</a></li> <li><a href="/wiki/LiveStation" title="LiveStation">LiveStation</a></li> <li><a href="/wiki/MyLifeBits" title="MyLifeBits">MyLifeBits</a></li> <li><a href="/wiki/Neural_Network_Intelligence" title="Neural Network Intelligence">Neural Network Intelligence</a></li> <li><a href="/wiki/NodeXL" title="NodeXL">NodeXL</a></li> <li><a href="/wiki/OneFuzz" title="OneFuzz">OneFuzz</a></li> <li><a href="/wiki/PhotoDNA" title="PhotoDNA">PhotoDNA</a></li> <li><a href="/wiki/Microsoft_SEAL" title="Microsoft SEAL">SEAL</a></li> <li><a href="/wiki/SLAM_project" title="SLAM project">SLAM</a></li> <li><a href="/wiki/T2_Temporal_Prover" title="T2 Temporal Prover">T2 Temporal Prover</a></li> <li><a href="/wiki/WorldWide_Telescope" title="WorldWide Telescope">WorldWide Telescope</a></li> <li><a href="/wiki/Z3_Theorem_Prover" title="Z3 Theorem Prover">Z3 Theorem Prover</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Operating_system" title="Operating system">Operating systems</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Barrelfish_(operating_system)" title="Barrelfish (operating system)">Barrelfish</a></li> <li><a href="/wiki/HomeOS" title="HomeOS">HomeOS</a></li> <li><a href="/wiki/Midori_(operating_system)" title="Midori (operating system)">Midori</a></li> <li><a href="/wiki/Singularity_(operating_system)" title="Singularity (operating system)">Singularity</a></li> <li><a href="/wiki/Verve_(operating_system)" title="Verve (operating system)">Verve</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/API" title="API">APIs</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Accelerator_(library)" title="Accelerator (library)">Accelerator</a></li> <li><a href="/wiki/Dryad_(programming)" title="Dryad (programming)">Dryad</a></li> <li><a href="/wiki/Joins_(concurrency_library)" title="Joins (concurrency library)">Joins</a></li> <li><a href="/wiki/Mimalloc" title="Mimalloc">mimalloc</a></li> <li><a href="/wiki/SXM_(transactional_memory)" title="SXM (transactional memory)">SXM</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Launched as products</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/C_Sharp_(programming_language)" title="C Sharp (programming language)">C#</a></li> <li><a href="/wiki/Microsoft_Comic_Chat" title="Microsoft Comic Chat">Comic Chat</a></li> <li><a href="/wiki/Microsoft_Detours" title="Microsoft Detours">Detours</a></li> <li><a href="/wiki/F_Sharp_(programming_language)" title="F Sharp (programming language)">F#</a></li> <li><a href="/wiki/Windows_Desktop_Gadgets" title="Windows Desktop Gadgets">Sideshow</a></li> <li><a href="/wiki/Microsoft_PixelSense" title="Microsoft PixelSense">PixelSense</a> (<a href="/wiki/TouchLight" title="TouchLight">TouchLight</a>)</li> <li><a href="/wiki/Microsoft_SenseCam" title="Microsoft SenseCam">SenseCam</a></li> <li><a href="/wiki/ClearType" title="ClearType">ClearType</a></li> <li><a href="/wiki/Group_Shot" title="Group Shot">Group Shot</a></li> <li><a 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0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Current</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Microsoft_Live_Labs_Pivot" title="Microsoft Live Labs Pivot">Pivot</a></li> <li><a href="/wiki/Seadragon_Software" title="Seadragon Software">Seadragon</a> <ul><li><a href="/wiki/Deep_Zoom" title="Deep Zoom">Deep Zoom</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Discontinued</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Microsoft_Live_Labs_Deepfish" title="Microsoft Live Labs Deepfish">Deepfish</a></li> <li><a href="/wiki/Microsoft_Live_Labs_Listas" title="Microsoft Live Labs Listas">Listas</a></li> <li><a href="/wiki/Live_Clipboard" title="Live Clipboard">Live Clipboard</a></li> <li><a href="/wiki/Photosynth" title="Photosynth">Photosynth</a></li> <li><a href="/wiki/Microsoft_Live_Labs_Volta" title="Microsoft Live Labs Volta">Volta</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Microsoft_FUSE_Labs" title="Microsoft FUSE Labs">FUSE Labs</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Docs.com" title="Docs.com">Docs.com</a></li> <li><a href="/wiki/Kodu_Game_Lab" title="Kodu Game Lab">Kodu</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other labs</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Microsoft_Academic_Search" title="Microsoft Academic Search">Academic Search</a></li> <li><a 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