CINXE.COM

<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.1 plus MathML 2.0 plus SVG 1.1//EN" "http://www.w3.org/2002/04/xhtml-math-svg/xhtml-math-svg-flat.dtd" > <html xmlns="http://www.w3.org/1999/xhtml"> <head> <title> Urs Schreiber in nLab </title> <meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /> <meta name="robots" content="index,follow" /> <meta name="viewport" content="width=device-width, initial-scale=1" /> <link href="/stylesheets/instiki.css?1676280126" media="all" rel="stylesheet" type="text/css" /> <link href="/stylesheets/mathematics.css?1660229990" media="all" rel="stylesheet" type="text/css" /> <link href="/stylesheets/syntax.css?1660229990" media="all" rel="stylesheet" type="text/css" /> <link href="/stylesheets/nlab.css?1676280126" media="all" rel="stylesheet" type="text/css" /> <link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/gh/dreampulse/computer-modern-web-font@master/fonts.css"/> <style type="text/css"> h1#pageName, div.info, .newWikiWord a, a.existingWikiWord, .newWikiWord a:hover, [actiontype="toggle"]:hover, #TextileHelp h3 { color: #226622; } a:visited.existingWikiWord { color: #164416; } </style> <style type="text/css"><![CDATA[/*></style> <script src="/javascripts/prototype.js?1660229990" type="text/javascript"></script> <script src="/javascripts/effects.js?1660229990" type="text/javascript"></script> <script src="/javascripts/dragdrop.js?1660229990" type="text/javascript"></script> <script src="/javascripts/controls.js?1660229990" type="text/javascript"></script> <script src="/javascripts/application.js?1660229990" type="text/javascript"></script> <script src="/javascripts/page_helper.js?1660229990" type="text/javascript"></script> <script src="/javascripts/thm_numbering.js?1660229990" type="text/javascript"></script> <script type="text/x-mathjax-config"> <![CDATA[//><!]]> </script> <script type="text/javascript"> <![CDATA[//><!]]> </script> <link href="https://ncatlab.org/nlab/atom_with_headlines" rel="alternate" title="Atom with headlines" type="application/atom+xml" /> <link href="https://ncatlab.org/nlab/atom_with_content" rel="alternate" title="Atom with full content" type="application/atom+xml" /> <script type="text/javascript"> document.observe("dom:loaded", function() { generateThmNumbers(); }); </script> </head> <body> <div id="Container"> <div id="Content"> <h1 id="pageName"> <span style="float: left; margin: 0.5em 0.25em -0.25em 0"> <svg xmlns="http://www.w3.org/2000/svg" width="1.872em" height="1.8em" viewBox="0 0 190 181"> <path fill="#226622" d="M72.8 145c-1.6 17.3-15.7 10-23.6 20.2-5.6 7.3 4.8 15 11.4 15 11.5-.2 19-13.4 26.4-20.3 3.3-3 8.2-4 11.2-7.2a14 14 0 0 0 2.9-11.1c-1.4-9.6-12.4-18.6-16.9-27.2-5-9.6-10.7-27.4-24.1-27.7-17.4-.3-.4 26 4.7 30.7 2.4 2.3 5.4 4.1 7.3 6.9 1.6 2.3 2.1 5.8-1 7.2-5.9 2.6-12.4-6.3-15.5-10-8.8-10.6-15.5-23-26.2-31.8-5.2-4.3-11.8-8-18-3.7-7.3 4.9-4.2 12.9.2 18.5a81 81 0 0 0 30.7 23c3.3 1.5 12.8 5.6 10 10.7-2.5 5.2-11.7 3-15.6 1.1-8.4-3.8-24.3-21.3-34.4-13.7-3.5 2.6-2.3 7.6-1.2 11.1 2.8 9 12.2 17.2 20.9 20.5 17.3 6.7 34.3-8 50.8-12.1z"/> <path fill="#a41e32" d="M145.9 121.3c-.2-7.5 0-19.6-4.5-26-5.4-7.5-12.9-1-14.1 5.8-1.4 7.8 2.7 14.1 4.8 21.3 3.4 12 5.8 29-.8 40.1-3.6-6.7-5.2-13-7-20.4-2.1-8.2-12.8-13.2-15.1-1.9-2 9.7 9 21.2 12 30.1 1.2 4 2 8.8 6.4 10.3 6.9 2.3 13.3-4.7 17.7-8.8 12.2-11.5 36.6-20.7 43.4-36.4 6.7-15.7-13.7-14-21.3-7.2-9.1 8-11.9 20.5-23.6 25.1 7.5-23.7 31.8-37.6 38.4-61.4 2-7.3-.8-29.6-13-19.8-14.5 11.6-6.6 37.6-23.3 49.2z"/> <path fill="#193c78" d="M86.3 47.5c0-13-10.2-27.6-5.8-40.4 2.8-8.4 14.1-10.1 17-1 3.8 11.6-.3 26.3-1.8 38 11.7-.7 10.5-16 14.8-24.3 2.1-4.2 5.7-9.1 11-6.7 6 2.7 7.4 9.2 6.6 15.1-2.2 14-12.2 18.8-22.4 27-3.4 2.7-8 6.6-5.9 11.6 2 4.4 7 4.5 10.7 2.8 7.4-3.3 13.4-16.5 21.7-16 14.6.7 12 21.9.9 26.2-5 1.9-10.2 2.3-15.2 3.9-5.8 1.8-9.4 8.7-15.7 8.9-6.1.1-9-6.9-14.3-9-14.4-6-33.3-2-44.7-14.7-3.7-4.2-9.6-12-4.9-17.4 9.3-10.7 28 7.2 35.7 12 2 1.1 11 6.9 11.4 1.1.4-5.2-10-8.2-13.5-10-11.1-5.2-30-15.3-35-27.3-2.5-6 2.8-13.8 9.4-13.6 6.9.2 13.4 7 17.5 12C70.9 34 75 43.8 86.3 47.4z"/> </svg> </span> <span class="webName">nLab</span> Urs Schreiber </h1> <div class="navigation"> <span class="skipNav"><a href='#navEnd'>Skip the Navigation Links</a> | </span> <span style="display:inline-block; width: 0.3em;"></span> <a href="/nlab/show/HomePage" accesskey="H" title="Home page">Home Page</a> | <a href="/nlab/all_pages" accesskey="A" title="List of all pages">All Pages</a> | <a href="/nlab/latest_revisions" accesskey="U" title="Latest edits and page creations">Latest Revisions</a> | <a href="https://nforum.ncatlab.org/discussion/14840/#Item_6" title="Discuss this page in its dedicated thread on the nForum" style="color: black">Discuss this page</a> | <a href="/nlab/author/Urs+Schreiber" style="color: black" title="Overview of nLab pages which Urs Schreiber has edited">Pages contributed to</a> <form accept-charset="utf-8" action="/nlab/search" id="navigationSearchForm" method="get"> <fieldset class="search"><input type="text" id="searchField" name="query" value="Search" style="display:inline-block; float: left;" onfocus="this.value == 'Search' ? this.value = '' : true" onblur="this.value == '' ? this.value = 'Search' : true" /></fieldset> </form> <span id='navEnd'></span> </div> <div id="revision"> <html xmlns="http://www.w3.org/1999/xhtml" xmlns:svg="http://www.w3.org/2000/svg" xml:lang="en" lang="en"> <head><meta http-equiv="Content-type" content="application/xhtml+xml;charset=utf-8" /><title>contents</title></head> <body><hr /> <p><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mspace width="thinmathspace"></mspace></mrow><annotation encoding="application/x-tex">\,</annotation></semantics></math></p> <div style="float:right;margin:0 20px 10px 20px;"><img width="230" src="http:ncatlab.org/nlab/files/Urs_Schreiber_portrait_Jan2024.jpg" alt="Urs Schreiber" /> </div> <h1 id="contents">contents</h1> <div class='maruku_toc'> <ul> <li><a href='#position'>position</a></li> <li><a href='#contact'>contact</a></li> <li><a href='#research'>research</a></li> <li><a href='#SelectedTalks'>selected talks</a></li> <li><a href='#publications'>publications:</a></li> <li><a href='#research_wiki'>research wiki</a></li> <li><a href='#more_web_logs'>more web logs</a></li> <li><a href='#teaching'>teaching</a></li> <li><a href='#column'>column</a></li> <li><a href='#joining_our_research'>joining our research</a></li> <li><a href='#CopyrightStatement'>copyright statement</a></li> </ul> </div> <div style="float:right;margin:0 20px 10px 20px;"> <a href="https://nyuad.nyu.edu/en/research/faculty-labs-and-projects/cqts.html"> <img src="https://ncatlab.org/schreiber/files/CQTS-logo_animated.gif" width="380" alt="animated logo of CQTS" /> </a> </div> <h2 id="position">position</h2> <p>I work in <br /> the <a href="https://nyuad.nyu.edu/en/academics/divisions/science/academic-programs/math.html">Mathematics Division of Science</a> <br /> of <a href="https://nyuad.nyu.edu/en/">New York University in Abu Dhabi</a> <br /> in the group of Prof. <a class="existingWikiWord" href="/nlab/show/Hisham+Sati">Hisham Sati</a> leading the <br /> <a href="https://nyuad.nyu.edu/en/research/faculty-labs-and-projects/cqts.html">Research Center for Quantum and Topological Systems</a> <br /> (see at <em><a class="existingWikiWord" href="/nlab/show/CQTS">CQTS</a></em> for latest activity).</p> <ul> <li><a href="https://nyuad.nyu.edu/en/research/faculty-labs-and-projects/cqts/urs-schreiber.html">page at NYU AD</a></li> </ul> <h2 id="contact">contact</h2> <ul> <li> <p><a href="mailto:us13@nyu.edu">us13@nyu.edu</a></p> </li> <li> <p><a href="mailto:urs.schreiber@gmail.com">urs.schreiber@gmail.com</a></p> </li> </ul> <h2 id="research">research</h2> <p>I am researching <a class="existingWikiWord" href="/nlab/show/mathematical+physics">mathematical</a> and <a class="existingWikiWord" href="/nlab/show/fundamental+physics">fundamental</a> <a class="existingWikiWord" href="/nlab/show/quantum+physics">quantum physics</a>, with a focus on using tools of <a class="existingWikiWord" href="/nlab/show/algebraic+topology">algebraic topology</a> and <a class="existingWikiWord" href="/schreiber/show/Higher+Topos+Theory+in+Physics">geometric homotopy theory</a> for understanding elusive <a class="existingWikiWord" href="/nlab/show/non-perturbative+quantum+field+theory">strongly-coupled</a> <a class="existingWikiWord" href="/nlab/show/quantum+systems">quantum systems</a> with applications to <a href="topological+quantum+computation#ReferencesNeedForTopologicalProtection">future</a> <a class="existingWikiWord" href="/nlab/show/topological+quantum+computing">topological</a> <a class="existingWikiWord" href="/nlab/show/quantum+technology">quantum technology</a>.</p> <p>Projects:</p> <ol> <li> <p><a class="existingWikiWord" href="/schreiber/show/Introduction+to+Hypothesis+H">Hypothesis H</a> on <a class="existingWikiWord" href="/nlab/show/geometry+of+physics+--+flux+quantization">flux quantization</a> in <a class="existingWikiWord" href="/nlab/show/M-theory">M-theory</a>.</p> </li> <li> <p><a class="existingWikiWord" href="/schreiber/show/Engineering+of+Anyons+on+M5-Probes">Geometric engineering of anyons on M5-branes</a><em>.</em></p> </li> <li> <p><a class="existingWikiWord" href="/schreiber/show/Quantum+Language+via+Linear+Homotopy+Types">Quantum language via linear homotopy types</a>.</p> </li> </ol> <h2 id="SelectedTalks">selected talks</h2> <blockquote> <p>For the complete list of invited talks I have given, see <a href="http://ncatlab.org/schreiber/show/differential+cohomology+in+a+cohesive+topos#References">there</a>.</p> </blockquote> <ul> <li> <p><strong><a class="existingWikiWord" href="/schreiber/show/Per%C3%AC+Panthe%C5%8Dr%C3%ADas">Perì Pantheōrías</a></strong></p> <p>guest appearance on <em><a href="https://www.youtube.com/channel/UCdWIQh9DGG6uhJk8eyIFl1w">Theories of Everything with Curt Jaimungal</a></em>, 8 March 2025</p> <p>video: <em><a href="https://youtu.be/1KUhLHlgG2Q">YT</a></em></p> </li> <li> <p><strong><a class="existingWikiWord" href="/schreiber/show/Quantum+Language+via+Linear+Homotopy+Types">Quantum Language via Linear Homotopy Types</a></strong></p> <p>mini-course at: <a href="http://www.q-math.es/conferences/IGQMA2025">IX International Workshop on Information Geometry, Quantum Mechanics and Applications 2025</a>, <a href="https://www.icmat.es/">ICMAT Madrid</a> 24-28 Feb 2025</p> <p>videos: <a href="https://www.youtube.com/playlist?list=PLLToCuSLUftnr8rAMkRaFlV85NoxoTlWx">YT</a></p> </li> <li> <p><strong><a class="existingWikiWord" href="/schreiber/show/Super-Exceptional+Geometry+for+11D+Supergravity">Super-Exceptional Geometry for 11D Supergravity</a></strong></p> <p><a href="https://seminars.aei.mpg.de/seminar/26232">talk in</a>: <a href="https://www.aei.mpg.de/358528/seminars-in-potsdam">HEP seminar</a> @ <a href="https://www.aei.mpg.de/">MPI for Gravitational Physics</a> (Dec 2024)</p> <p>video: <a href="https://youtu.be/iayDIBPXTf4">YT</a></p> </li> <li> <p><strong><a class="existingWikiWord" href="/schreiber/show/Higher+Topos+Theory+in+Physics">Higher Topos Theory in Physics</a></strong></p> <p><a href="https://researchseminars.org/talk/CaTheoryZulip/5/">talk in</a>: <a href="https://researchseminars.org/seminar/CaTheoryZulip">Zulip Category Theory Seminar</a> (Jun 2024)</p> <p>video: <a href="https://youtu.be/Gr_BCr1rYVM">YT</a></p> </li> <li> <p><strong><a class="existingWikiWord" href="/schreiber/show/Towards+Certified+Topological+Quantum+Programming+via+Linear+Homotopy+Types">Towards Certified Topological Quantum Programming via Linear Homotopy Types</a></strong></p> <p>talk at: <a href="https://ncatlab.org/nlab/show/Center+for+Quantum+and+Topological+Systems#QuantumConference2024">Quantum Information and Quantum Matter 2024</a>, NYUAD (May 2024)</p> </li> <li> <p><strong><a href="/schreiber/show/Topological+Quantum+Gates+in+Homotopy+Type+Theory#HoTTEST2024">Topological Quantum Programming with Linear Homotopy Types</a></strong></p> <p>talk at: <em><a href="https://www.uwo.ca/math/faculty/kapulkin/seminars/hottest.html">Homotopy Type Theory Electronic Seminar,</a></em>, 02 Feb 2024</p> <p>video: <a href="https://youtu.be/Wnm3yCUzNb0">YT</a></p> </li> <li> <p><strong><a class="existingWikiWord" href="/schreiber/show/Introduction+to+Hypothesis+H">Introduction to Quantum Hypothesis H</a></strong></p> <p>talk at: <em><a href="https://ncatlab.org/nlab/show/M-Theory+and+Mathematics#2024">M-Theory and Mathematics 2024</a></em>, Jan 2024</p> <p>video: <a href="https://cdnapisec.kaltura.com/html5/html5lib/v2.73.2/mwEmbedFrame.php/p/1674401/uiconf_id/23435151/entry_id/1_ysnxjdbb?wid=_1674401&iframeembed=true&playerId=kaltura_player&entry_id=1_ysnxjdbb">kt</a></p> </li> <li> <p><strong><a class="existingWikiWord" href="/schreiber/show/Higher+Topos+Theory+in+Physics">Higher Topos Theory in Physics</a></strong></p> <p>talk at: <a href="https://education.wolfram.com/winter-school/">Wolfram Science Winter School</a>, Jan 2024</p> <p>video: <a href="https://youtu.be/GD20W6vxMI4">YT</a></p> </li> <li> <p><strong><a class="existingWikiWord" href="/schreiber/show/Topological+Quantum+Gates+in+Homotopy+Type+Theory">Topological Quantum Gates in Homotopy Type Theory</a></strong></p> <p><a href="https://ncatlab.org/nlab/show/Center+for+Quantum+and+Topological+Systems#SchreiberMar2023">talk at</a>: <em><a href="https://ncatlab.org/nlab/show/Center+for+Quantum+and+Topological+Systems#ConferencesMar2023">QFT and Cobordism 2023</a></em></p> <p>video: <a href="https://www.youtube.com/watch?v=pu5bpJ263X0">YT</a></p> </li> <li> <p><strong><a class="existingWikiWord" href="/schreiber/show/Higher+Topos+Theory+in+Physics">Higher Topos Theory in Physics</a></strong></p> <p><a href="https://ncatlab.org/nlab/show/Center+for+Quantum+and+Topological+Systems#SchreiberOct2023">talk at</a>: <em><a href="https://ncatlab.org/nlab/show/Center+for+Quantum+and+Topological+Systems#oct_2023">Workshop on Homotopy Theory and Applications</a></em></p> <p>video: <a href="https://youtu.be/wNhoAiITJQs">YT</a></p> </li> <li> <p><strong><a class="existingWikiWord" href="/schreiber/show/Topological+Quantum+Gates+from+M-Theory">Topological Quantum Gates from M-Theory</a></strong></p> <p><a href="M-Theory+and+Mathematics#Schreiber2023">talk at</a>: <em><a href="M-Theory+and+Mathematics#2023">M-Theory and Mathematics 2023</a></em></p> <p>video: <a href="https://www.youtube.com/watch?v=Ob9tOgWumPI">YT</a></p> </li> <li> <p><strong><a class="existingWikiWord" href="/schreiber/show/Topological+Quantum+Programming+in+TED-K">Topological Quantum Programming in TED-K</a></strong></p> <p><a href="https://planqc2022.hotcrp.com/paper/33">talk at</a>: <em><a href="https://icfp22.sigplan.org/home/planqc-2022">PlanQC 2022</a></em></p> <p>video: <a href="https://www.youtube.com/watch?v=hDwXQVcloB8&feature=emb_logo">YT</a></p> </li> </ul> <h2 id="publications">publications:</h2> <p>For comprehensive lists see:</p> <ul> <li> <p><a href="https://inspirehep.net/authors/1056029">at inSpire</a></p> </li> <li> <p><a href="https://scholar.google.com/citations?hl=en&user=bDfHFDcAAAAJ">at GoogleScholar</a></p> </li> <li> <p><a href="https://arxiv.org/find/math/1/au:+Schreiber_U/0/1/0/all/0/1">at arXiv.org</a></p> </li> </ul> <p>Monographs:</p> <div style="float:right;margin:0px 0px 0px 20px;"> <a href="https://doi.org/10.1142/13422 "><img src="https://ncatlab.org/schreiber/files/CharacterMap-WSCover.jpg" width="300" /></a> </div> <ul> <li> <p><strong><a class="existingWikiWord" href="/schreiber/show/The+Character+Map+in+Non-Abelian+Cohomology">The Character Map in Non-Abelian Cohomology</a></strong></p> <p>(with <a class="existingWikiWord" href="/nlab/show/Domenico+Fiorenza">D. Fiorenza</a> & <a class="existingWikiWord" href="/nlab/show/Hisham+Sati">H. Sati</a>)</p> <p>World Scientific (2023)</p> <p>[<a href="https://doi.org/10.1142/13422">doi:10.1142/13422</a>]</p> </li> </ul> <blockquote> <p id="Blurb"> <strong>Cover blurb:</strong> This book presents a novel development of fundamental and fascinating aspects of <a class="existingWikiWord" href="/nlab/show/algebraic+topology">algebraic topology</a> and <a class="existingWikiWord" href="/nlab/show/mathematical+physics">mathematical physics</a>: “<a class="existingWikiWord" href="/nlab/show/Whitehead-generalized+cohomology">extra-ordinary</a>” and further <a class="existingWikiWord" href="/nlab/show/generalized+cohomology+theories">generalized cohomology theories</a> enhanced to “<a class="existingWikiWord" href="/nlab/show/twisted+cohomology">twisted</a>” and <a class="existingWikiWord" href="/nlab/show/differential+cohomology">differential</a>-geometric form with focus on their <a class="existingWikiWord" href="/nlab/show/rational+homotopy+theory">rational approximation</a> by <a class="existingWikiWord" href="/nlab/show/Chern-Dold+character">generalized Chern character</a> maps and on the resulting <a class="existingWikiWord" href="/nlab/show/charge+quantization">charge quantization</a> laws in <a class="existingWikiWord" href="/nlab/show/higher+gauge+theory">higher <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"> <semantics> <mrow> <mi>n</mi> </mrow> <annotation encoding="application/x-tex">n</annotation> </semantics> </math>-form gauge field theories</a> appearing in <a class="existingWikiWord" href="/nlab/show/string+theory">string theory</a> and in the <a class="existingWikiWord" href="/nlab/show/K-theory+classification+of+topological+phases+of+matter">classification of</a> <a class="existingWikiWord" href="/nlab/show/topological+phase+of+matter">topological</a> <a class="existingWikiWord" href="/nlab/show/quantum+materials">quantum materials</a>.</p> <p>Motivation for the conceptual re-development is the observation, laid out in the introductory chapter, that famous and famously elusive effects in strongly interacting (“<a class="existingWikiWord" href="/nlab/show/non-perturbative+physics">non-perturbative</a>”) <a class="existingWikiWord" href="/nlab/show/quantum+field+theory">physics</a> demand “<a class="existingWikiWord" href="/nlab/show/non-abelian+cohomology">non-abelian</a>” generalization of much of established <a class="existingWikiWord" href="/nlab/show/generalized+cohomology+theory">generalized cohomology theory</a>. But the relevant higher <a class="existingWikiWord" href="/nlab/show/non-abelian+cohomology">non-abelian cohomology</a> theory (”<a class="existingWikiWord" href="/nlab/show/principal+infinity-bundle">higher gerbes</a>“) has an esoteric reputation and has remained underdeveloped.</p> <p>The book’s theme is that variously <a class="existingWikiWord" href="/nlab/show/generalized+cohomology+theories">generalized cohomology theories</a> are <a class="existingWikiWord" href="/nlab/show/cohomology">best viewed</a> through their <a class="existingWikiWord" href="/nlab/show/classifying+spaces">classifying spaces</a> – possibly but not necessarily <a class="existingWikiWord" href="/nlab/show/infinite-loop+spaces">infinite-loop spaces</a> – from which perspective the <a class="existingWikiWord" href="/nlab/show/Chern-Dold+character">character map</a> is really an incarnation of the <a class="existingWikiWord" href="/nlab/show/fundamental+theorem+of+dg-algebraic+rational+homotopy+theory">fundamental theorem of rational homotopy theory</a>, thereby uniformly subsuming not only the classical <a class="existingWikiWord" href="/nlab/show/Chern+character">Chern character</a> and a multitude of scattered variants that have been proposed, but now seamlessly applying in the previously elusive generality of (<a class="existingWikiWord" href="/nlab/show/twisted+cohomology">twisted</a>, <a class="existingWikiWord" href="/nlab/show/differential+cohomology">differential</a> and) <a class="existingWikiWord" href="/nlab/show/non-abelian+cohomology">non-abelian cohomology</a>.</p> <p>In laying out this result with plenty of examples, we provide modernized introduction and review of fundamental classical topics: 1. abstract <a class="existingWikiWord" href="/nlab/show/homotopy+theory">homotopy theory</a> via <a class="existingWikiWord" href="/nlab/show/model+categories">model categories</a>, 2. <a class="existingWikiWord" href="/nlab/show/generalized+cohomology">generalized cohomology</a> in <a class="existingWikiWord" href="/nlab/show/homotopy+theory">homotopical</a> incarnation, 3. <a class="existingWikiWord" href="/nlab/show/dg-algebra">dg-algebraic</a> <a class="existingWikiWord" href="/nlab/show/rational+homotopy+theory">rational homotopy theory</a>, whose <a class="existingWikiWord" href="/nlab/show/fundamental+theorem+of+dg-algebraic+rational+homotopy+theory">fundamental theorem</a> we re-cast as a (twisted) non-abelian <a class="existingWikiWord" href="/nlab/show/de+Rham+theorem">de Rham theorem</a> which naturally induces the (twisted) non-abelian character map.</p> </blockquote> <p><br /></p> <div style="float:right;margin:-60px -120px 0px 20px;"> <a href="https://doi.org/10.1142/13422 "><img src="https://ncatlab.org/schreiber/files/EquivariantInfinityBundlesDiagram.jpg" width="670" /></a> </div> <ul> <li> <p><strong><a class="existingWikiWord" href="/schreiber/show/Equivariant+principal+infinity-bundles">Equivariant Principal <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"> <semantics> <mrow> <mn>∞</mn> </mrow> <annotation encoding="application/x-tex">\infty</annotation> </semantics> </math>-Bundles</a></strong></p> <p>(with <a class="existingWikiWord" href="/nlab/show/Hisham+Sati">H. Sati</a>)</p> <p>Cambridge University Press</p> <p>(2025, in print)</p> </li> </ul> <p><br /></p> <ul> <li> <p>further monographs on the <a class="existingWikiWord" href="/nlab/show/nLab">nLab</a>:</p> <ul> <li> <p><em><a class="existingWikiWord" href="/schreiber/show/Introduction+to+Homological+algebra">Introduction to Homological algebra</a></em></p> </li> <li> <p><em><a class="existingWikiWord" href="/nlab/show/Introduction+to+Stable+homotopy+theory">Introduction to Stable homotopy theory</a></em></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/geometry+of+physics+--+categories+and+toposes">geometry of physics – categories and toposes</a></p> </li> </ul> </li> <li> <p>other:</p> <ul> <li> <p><em><a class="existingWikiWord" href="/schreiber/show/Higher+Prequantum+Geometry">Higher Prequantum Geometry</a></em>, in: <em><a class="existingWikiWord" href="/nlab/show/New+Spaces+for+Mathematics+and+Physics">New Spaces for Mathematics and Physics</a></em>, Cambr. Univ. Press (2021) <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mo stretchy="false">[</mo></mrow><annotation encoding="application/x-tex">[</annotation></semantics></math><a href="https://doi.org/10.1017/9781108854429">doi:10.1017/9781108854429</a><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">]</annotation></semantics></math></p> </li> <li> <p><em><a class="existingWikiWord" href="/schreiber/show/Mathematical+Foundations+of+Quantum+Field+and+Perturbative+String+Theory">Mathematical Foundations of Quantum Field and Perturbative String Theory</a></em>, Proceedings of Symposia in Pure Mathematics <strong>83</strong> Amer. Math. Soc (2011) <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mo stretchy="false">[</mo></mrow><annotation encoding="application/x-tex">[</annotation></semantics></math><a href="http://bookstore.ams.org/PSPUM-83">ISBN:978-0-8218-5195-1</a><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">]</annotation></semantics></math></p> </li> </ul> </li> </ul> <p><br /></p> <h2 id="research_wiki">research wiki</h2> <p><a href="http://ncatlab.org/nlab/show/HomePage"><div style="float:right;margin:0 20px 10px 20px;"><img width="250" src="/nlab/files/OldnLabBanner.jpg" alt="nLab banner" /></div></a></p> <p>For making notes on math/phys I had started (in Nov 2008)</p> <ul> <li><em><a class="existingWikiWord" href="/nlab/show/Home+Page">the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"> <semantics> <mrow> <mi>n</mi> </mrow> <annotation encoding="application/x-tex">n</annotation> </semantics> </math>Lab research wiki project</a></em></li> </ul> <p>with edit logs and discussion being had on:</p> <ul> <li><a href="https://nforum.ncatlab.org/">the nForum discussion board</a>.</li> </ul> <p>For more on the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math>Lab, see:</p> <ul> <li> <p>me on: <em><a class="existingWikiWord" href="/schreiber/show/What+is...+the+nLab">What is… the nLab?</a></em></p> <p>(presentation at: <em><a href="http://math.bu.edu/people/matschke/BigDataPureMath2022/">Big Data in Pure Mathematics 2022</a></em>)</p> </li> <li> <p>Wikipedia on: <em><a href="http://en.wikipedia.org/wiki/NLab">nLab</a></em>.</p> </li> </ul> <h2 id="more_web_logs">more web logs</h2> <p>For logs of further activity see:</p> <ul> <li> <p><a href="https://twitter.com/UrsSchreiber">my feed at X/Twitter</a> (new)</p> </li> <li> <p><a href="https://twitter.com/SchreiberUrs">my old feed at X/Twitter</a> (lost my password…)</p> </li> <li> <p><a href="https://www.youtube.com/@UrsSchreiber">my channel on YouTube</a></p> </li> </ul> <p>while <a class="existingWikiWord" href="/nlab/show/nLab"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"> <semantics> <mrow> <mi>n</mi> </mrow> <annotation encoding="application/x-tex">n</annotation> </semantics> </math>Lab</a>-edits are announced</p> <ul> <li><em><a href="https://nforum.ncatlab.org/">on the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math>Forum</a></em>.</li> </ul> <p>For links to technical discussions about math and physics see my pages:</p> <ul> <li> <p><em><a href="http://mathoverflow.net/users/381/urs-schreiber">at MathOverflow</a></em></p> </li> <li> <p><em><a href="http://www.physicsoverflow.org/user/Urs+Schreiber">at PhysicsOverflow</a></em></p> </li> <li> <p><em><a href="http://physics.stackexchange.com/users/5603/urs-schreiber">at Physics.SE</a></em></p> </li> <li> <p><em><a href="https://quantumcomputing.stackexchange.com/users/19363/urs-schreiber">at QuantumComputing.SE</a>.</em></p> </li> </ul> <h2 id="teaching">teaching</h2> <p>See behind these links for lecture notes that I wrote:</p> <table><thead><tr><th>date</th><th>lecture notes</th></tr></thead><tbody><tr><td style="text-align: left;">winter <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mspace width="thinmathspace"></mspace><mspace width="thinmathspace"></mspace></mrow><annotation encoding="application/x-tex">\,\,</annotation></semantics></math> 2017</td><td style="text-align: left;"><em><a class="existingWikiWord" href="/schreiber/show/Mathematical+Quantum+Field+Theory">Mathematical Quantum Field Theory</a></em></td></tr> <tr><td style="text-align: left;">summer 2017</td><td style="text-align: left;"><em><a class="existingWikiWord" href="/schreiber/show/Topological+K-Theory">Topological K-Theory</a></em></td></tr> <tr><td style="text-align: left;">summer 2017</td><td style="text-align: left;"><em><a class="existingWikiWord" href="/nlab/show/Introduction+to+Topology">Topology</a></em></td></tr> <tr><td style="text-align: left;">winter <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mspace width="thinmathspace"></mspace><mspace width="thinmathspace"></mspace></mrow><annotation encoding="application/x-tex">\,\,</annotation></semantics></math> 2016</td><td style="text-align: left;"><em><a class="existingWikiWord" href="/schreiber/show/From+the+Superpoint+to+T-Folds">Super Cartan Geometry</a></em></td></tr> <tr><td style="text-align: left;">summer 2016</td><td style="text-align: left;"><em><a class="existingWikiWord" href="/nlab/show/Introduction+to+Stable+homotopy+theory+--+S">Complex oriented cohomology theory</a></em></td></tr> <tr><td style="text-align: left;">summer 2016</td><td style="text-align: left;"><em><a class="existingWikiWord" href="/nlab/show/Introduction+to+Stable+homotopy+theory">Stable Homotopy Theory</a></em></td></tr> <tr><td style="text-align: left;">summer 2015</td><td style="text-align: left;"><em><a class="existingWikiWord" href="/schreiber/show/Structure+Theory+for+Higher+WZW+Terms">Structure Theory for Higher WZW Terms</a></em></td></tr> <tr><td style="text-align: left;">summer 2015</td><td style="text-align: left;"><em><a class="existingWikiWord" href="/schreiber/show/Higher+Cartan+Geometry">Higher Cartan Geometry</a></em></td></tr> <tr><td style="text-align: left;">summer 2014</td><td style="text-align: left;"><em><a class="existingWikiWord" href="/schreiber/show/HAI">Homological Algebra</a></em></td></tr> </tbody></table> <p>A list of further teaching in the past is <em><a href="http://ncatlab.org/schreiber/show/HomePage#Teaching">here</a></em>.</p> <h2 id="column">column</h2> <p>I used to write an irregular column at <a href="https://www.physicsforums.com/insights/">PhysicsForums Insights</a>. Articles in the series include these:</p> <p><strong>on pre-quantum field theory</strong></p> <ul> <li> <p><em><a href="https://www.physicsforums.com/insights/higher-prequantum-geometry-need-prequantum-geometry/">Higher prequantum geometry I: The need for prequantum geometry</a></em></p> </li> <li> <p><em><a href="https://www.physicsforums.com/insights/higher-prequantum-geometry-ii-principle-extremal-action-comonadically/#toggle-id-1">Higher prequantum geometry II: The principle of extremal action – Comonadically</a></em></p> </li> <li> <p><em><a href="https://www.physicsforums.com/insights/higher-prequantum-geometry-iii-global-action-functional-cohomologically/">Higher prequantum geometry III: The global action functional – Cohomologically</a></em></p> </li> <li> <p><em><a href="https://www.physicsforums.com/insights/higher-prequantum-geometry-iv-covariant-phase-space-transgressively/">Higher prequantum geometry IV: The covariant phase space – Transgressively</a></em></p> </li> <li> <p><em><a href="https://www.physicsforums.com/insights/higher-prequantum-geometry-v-local-observables-lie-theoretically/">Higher prequantum geometry V: The local observables – Lie theoretically</a></em></p> </li> <li> <p><em><a href="https://www.physicsforums.com/insights/examples-prequantum-field-theories-gauge-fields/">Examples of Prequantum field theories I: Gauge fields</a></em></p> </li> <li> <p><em><a href="https://www.physicsforums.com/insights/examples-prequantum-field-theories-ii-higher-gauge-fields/">Examples of Prequantum field theories II: Higher gauge fields</a></em></p> </li> <li> <p><em><a href="https://www.physicsforums.com/insights/examples-prequantum-field-theories-iii-chern-simons-type-theories/">Examples of Prequantum field theories III: Chern-Simons-type theories</a></em></p> </li> <li> <p><em><a href="https://www.physicsforums.com/insights/examples-prequantum-field-theories-iv-wess-zumino-witten-type-theories/">Examples of Prequantum field theories IV: Wess-Zumino-Witten-type theories</a></em></p> </li> </ul> <p><strong>on perturbative quantum field theory</strong></p> <ul> <li><em><a href="https://www.physicsforums.com/insights/paqft-idea-references/">Introduction to Perturbative Quantum Field Theory</a></em></li> </ul> <p><strong>on string theory</strong></p> <ul> <li> <p><em><a href="https://www.physicsforums.com/insights/20-years-ago-today-m-theory-conjecture/">It was 20 years ago today – the M-theory conjecture</a></em></p> </li> <li> <p><em><a href="https://www.physicsforums.com/insights/homotopy-lie-n-algebras-supergravity/">Homotopy Lie n-algebras in Supergravity</a></em></p> </li> <li> <p><em><a href="https://www.physicsforums.com/insights/emergence-from-the-superpoint/">Emergence from the superpoint</a></em></p> </li> <li> <p><em><a href="https://www.physicsforums.com/insights/supersymmetry-delignes-theorem/">Why supersymmetry? Because of Deligne’s theorem</a></em></p> </li> <li> <p><em><a href="https://www.physicsforums.com/insights/11d-gravity-just-torsion-constraint/">11d Gravity from just the Torsion Constraint</a></em></p> </li> <li> <p><em><a href="https://www.physicsforums.com/insights/spectral-standard-model-string-compactifications/">Spectral Standard Model and String Compactifications</a></em></p> </li> <li> <p><em><a href="https://www.physicsforums.com/insights/higher-category-theory-physics/">Why Higher Category Theory in Physics?</a></em></p> </li> <li> <p><em><a href="http://www.physicsforums.com/insights/super-p-brane-theory-emerging-super-homotopy-theory/">Super p-Brane Theory from Super Homotopy Theory</a></em></p> </li> </ul> <h2 id="joining_our_research">joining our research</h2> <p>If you are a graduate student or young postdoc thinking of entering the Sati-Schreiber program, here is some basic reading to start with:</p> <ul> <li> <p>for relevant basics of general <a class="existingWikiWord" href="/nlab/show/homotopy+theory">homotopy theory</a> and <a class="existingWikiWord" href="/nlab/show/infinity-stacks"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"> <semantics> <mrow> <mn>∞</mn> </mrow> <annotation encoding="application/x-tex">\infty</annotation> </semantics> </math>-stacks</a>/<a class="existingWikiWord" href="/nlab/show/smooth+infinity-groupoids">smooth <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"> <semantics> <mrow> <mn>∞</mn> </mrow> <annotation encoding="application/x-tex">\infty</annotation> </semantics> </math>-groupoids</a>:</p> <p>see the chapter <em>Model categories</em> in <em><a class="existingWikiWord" href="/schreiber/show/The+Character+Map+in+Non-Abelian+Cohomology">The Character Map in Non-Abelian Cohomology</a></em> (chapter 1 in the printed version, appendix in the arXiv version)</p> <p>and for more details the nLab entries <em><a class="existingWikiWord" href="/nlab/show/Introduction+to+Homotopy+Theory">Introduction to Homotopy Theory</a></em> or for yet more details <em><a class="existingWikiWord" href="/nlab/show/geometry+of+physics+--+categories+and+toposes">geometry of physics – categories and toposes</a></em></p> </li> <li> <p>for relevant basics of <a class="existingWikiWord" href="/nlab/show/rational+homotopy+theory">rational homotopy theory</a> and <a class="existingWikiWord" href="/nlab/show/L-infinity+algebras"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"> <semantics> <mrow> <msub><mi>L</mi> <mn>∞</mn></msub> </mrow> <annotation encoding="application/x-tex">L_\infty</annotation> </semantics> </math>-Lie algebras</a>:</p> <p>see the part <em>Non-abelian de Rham cohomology</em> in <em><a class="existingWikiWord" href="/schreiber/show/The+Character+Map+in+Non-Abelian+Cohomology">The Character Map in Non-Abelian Cohomology</a></em></p> </li> <li> <p>for relevant basics of <a class="existingWikiWord" href="/nlab/show/supergravity">supergravity</a> and <a class="existingWikiWord" href="/nlab/show/super+p-branes">super <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"> <semantics> <mrow> <mi>p</mi> </mrow> <annotation encoding="application/x-tex">p</annotation> </semantics> </math>-branes</a>:</p> <p>see the articles <em><a class="existingWikiWord" href="/schreiber/show/Flux+Quantization+on+11d+Superspace">Flux Quantization on 11d Superspace</a></em> and <em><a class="existingWikiWord" href="/schreiber/show/Flux+Quantization+on+M5-Branes">Flux Quantization on M5-Branes</a></em></p> <p>and/or the nLab entry <em><a class="existingWikiWord" href="/nlab/show/geometry+of+physics+--+supergeometry+and+superphysics">geometry of physics – supergeometry and superphysics</a></em></p> </li> </ul> <h2 id="CopyrightStatement">copyright statement</h2> <blockquote> <p>To the extent that it matters, my contributions to the <a class="existingWikiWord" href="/nlab/show/HomePage">nLab</a> are copyrighted according to <a href="https://creativecommons.org/licenses/by-sa/3.0/">CC BY-SA 3.0</a>.</p> </blockquote> <p><br /></p> <p><br /></p> <hr /> <p><br /></p> <p><br /></p> <div class="property">category: <a class="category_link" href="/nlab/all_pages/people">people</a></div></body></html> </div> <div class="revisedby"> <p> Last revised on March 20, 2025 at 14:02:21. See the <a href="/nlab/history/Urs+Schreiber" style="color: #005c19">history</a> of this page for a list of all contributions to it. </p> </div> <div class="navigation navfoot"> <a href="/nlab/edit/Urs+Schreiber" accesskey="E" class="navlink" id="edit" rel="nofollow">Edit</a><a href="https://nforum.ncatlab.org/discussion/14840/#Item_6">Discuss</a><span class="backintime"><a href="/nlab/revision/Urs+Schreiber/115" accesskey="B" class="navlinkbackintime" id="to_previous_revision" rel="nofollow">Previous revision</a></span><a href="/nlab/show/diff/Urs+Schreiber" accesskey="C" class="navlink" id="see_changes" rel="nofollow">Changes from previous revision</a><a href="/nlab/history/Urs+Schreiber" accesskey="S" class="navlink" id="history" rel="nofollow">History (115 revisions)</a> <a href="/nlab/show/Urs+Schreiber/cite" style="color: black">Cite</a> <a href="/nlab/print/Urs+Schreiber" accesskey="p" id="view_print" rel="nofollow">Print</a> <a href="/nlab/source/Urs+Schreiber" id="view_source" rel="nofollow">Source</a> </div> </div>  </div>  </body> </html>