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Yuri Manin in nLab
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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/11943/#Item_4" title="Discuss this page in its dedicated thread on the nForum" style="color: black">Discuss this page</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></title></head> <body> <p>Yuri Ivanovich Manin (1937-2023, Russian: Юрий Иванович Манин) was a Russian-born mathematician of polymath broadness, with main works in <a class="existingWikiWord" href="/nlab/show/number+theory">number theory</a> and <a class="existingWikiWord" href="/nlab/show/arithmetic+geometry">arithmetic geometry</a>, <a class="existingWikiWord" href="/nlab/show/noncommutative+geometry">noncommutative geometry</a>, <a class="existingWikiWord" href="/nlab/show/algebraic+geometry">algebraic geometry</a> and <a class="existingWikiWord" href="/nlab/show/mathematical+physics">mathematical physics</a>.</p> <ul> <li> <p><a href="http://en.wikipedia.org/wiki/Yuri_I._Manin">Wikipedia entry</a></p> </li> <li> <p><a href="https://www.mpim-bonn.mpg.de/node/11864">MPI obituary</a></p> </li> </ul> <p>His diverse work includes a classification theorem in the theory of commutative <a class="existingWikiWord" href="/nlab/show/formal+group">formal group</a>, early study of monoidal transformations and exposition on <a class="existingWikiWord" href="/nlab/show/motive">motive</a>s in 1960-s, a fundamental starting work in <a class="existingWikiWord" href="/nlab/show/quantum+information+theory">quantum information theory</a>, proposals on <a class="existingWikiWord" href="/nlab/show/quantum+logic">quantum logic</a>s, an approach to <a class="existingWikiWord" href="/nlab/show/quantum+group">quantum group</a>s, ADHM construction in <a class="existingWikiWord" href="/nlab/show/soliton">soliton</a> theory, work with <a class="existingWikiWord" href="/nlab/show/Maxim+Kontsevich">Maxim Kontsevich</a> on <a class="existingWikiWord" href="/nlab/show/Gromov-Witten+invariants">Gromov-Witten invariants</a>, work on <a class="existingWikiWord" href="/nlab/show/Frobenius+manifold">Frobenius manifold</a>s (and introduced more general “F-manifolds” with Claus Hertling). He published a number of influential monographs including on <a class="existingWikiWord" href="/nlab/show/noncommutative+geometry">noncommutative geometry</a>, <a class="existingWikiWord" href="/nlab/show/quantum+group">quantum group</a>s, <a class="existingWikiWord" href="/nlab/show/complex+geometry">complex geometry</a> and <a class="existingWikiWord" href="/nlab/show/gauge+theory">gauge theories</a>, introduction to <a class="existingWikiWord" href="/nlab/show/scheme">scheme</a>s, <a class="existingWikiWord" href="/nlab/show/Frobenius+manifold">Frobenius manifold</a>s, mathematical <a class="existingWikiWord" href="/nlab/show/logic">logic</a>s…</p> <p>Manin’s students include:</p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/A.+Beilinson">A. Beilinson</a>,</p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/V.+Drinfel%27d">V. Drinfel'd</a></p> </li> <li> <p>Vera Serganova</p> </li> <li> <p>Ivan Penkov</p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/M.+Kapranov">M. Kapranov</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Yuri+Tschinkel">Yuri Tschinkel</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Ralph+Kaufmann">Ralph Kaufmann</a></p> </li> <li> <p>…</p> </li> </ul> <h2 id="selected_writings">Selected writings</h2> <p>Introducing what came to be called the <em><a class="existingWikiWord" href="/nlab/show/Gauss-Manin+connection">Gauss-Manin connection</a></em>:</p> <ul> <li id="Manin58"><a class="existingWikiWord" href="/nlab/show/Yuri+Manin">Yuri Manin</a>, <em>Algebraic curves over fields with differentiation</em>, Izv. Akad. Nauk SSSR Ser. Mat. <strong>22</strong> 6 (1958) 737-756 <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://mi.mathnet.ru/izv3998">mathnet:izv3998</a>, <a href="http://www.mathnet.ru/php/getFT.phtml?jrnid=im&paperid=3998&volume=22&year=1958&issue=6&fpage=737&what=fullt&option_lang=eng">pdf</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> (in Russian)</li> </ul> <p>Introducing the <a class="existingWikiWord" href="/nlab/show/ADHM+construction">ADHM construction</a> for <a class="existingWikiWord" href="/nlab/show/Yang-Mills+instantons">Yang-Mills instantons</a>:</p> <ul> <li><a class="existingWikiWord" href="/nlab/show/Michael+Atiyah">Michael Atiyah</a>, <a class="existingWikiWord" href="/nlab/show/Nigel+Hitchin">Nigel Hitchin</a>, <a class="existingWikiWord" href="/nlab/show/Vladimir+Drinfeld">Vladimir Drinfeld</a>, <a class="existingWikiWord" href="/nlab/show/Yuri+Manin">Yuri Manin</a>, <em>Construction of instantons</em>, Physics Letters A <strong>65</strong> 3 (1978) 185-187 [<a href="https://doi.org/10.1016/0375-9601(78)90141-X">doi:10.1016/0375-9601(78)90141-X</a>]</li> </ul> <p>Introducing the notion of <a class="existingWikiWord" href="/nlab/show/quantum+computation">quantum computation</a>:</p> <ul> <li id="Manin1980"><a class="existingWikiWord" href="/nlab/show/Yuri+I.+Manin">Yuri I. Manin</a>, Introduction to: <em>Computable and Uncomputable</em>, Sov. Radio (1980) [Russian original: <a class="existingWikiWord" href="/nlab/files/Manin-1980.pdf" title="pdf">pdf</a>], English translation on p. 69-77 of <em>Mathematics as Metaphor: Selected essays of Yuri I. Manin</em>, Collected Works <strong>20</strong>, AMS (2007) [<a href="https://bookstore.ams.org/cworks-20/">ISBN:978-0-8218-4331-4</a>] <blockquote> <p>Perhaps, for a better understanding of [molecular biology], we need a mathematical theory of quantum automata.</p> </blockquote> </li> </ul> <p>and review of <a class="existingWikiWord" href="/nlab/show/Shor%27s+algorithm">Shor's algorithm</a>:</p> <ul> <li><a class="existingWikiWord" href="/nlab/show/Yuri+I.+Manin">Yuri I. Manin</a>, <em>Classical computing, quantum computing, and Shor’s factoring algorithm</em>, Astérisque, <strong>266</strong> Séminaire Bourbaki 862 (2000) 375-404 [<a href="https://arxiv.org/abs/quant-ph/9903008">arXiv:quant-ph/9903008</a>, <a href="http://www.numdam.org/item/?id=SB_1998-1999__41__375_0">numdam:SB_1998-1999__41__375_0</a>]</li> </ul> <p>Early discussion of mathematical <a class="existingWikiWord" href="/nlab/show/supergeometry">supergeometry</a>:</p> <ul> <li><a class="existingWikiWord" href="/nlab/show/Yuri+Manin">Yuri Manin</a>, <em><a class="existingWikiWord" href="/nlab/show/New+Dimensions+in+Geometry">New Dimensions in Geometry</a></em>, in: <em>Arbeitstagung Bonn 1984</em>, Lecture Notes in Mathematics <strong>1111</strong>, Springer (1985) 59–101 [<a href="[doi:10.1007/BFb0084585](https://doi.org/10.1007/BFb0084585">doi:10.1007/BFb0084585)</a>, <a href="http://people.mpim-bonn.mpg.de/zagier/files/doi/10.1007/BFb0084581/chapter04.pdf">pdf</a>]</li> </ul> <p>On the <a class="existingWikiWord" href="/nlab/show/Penrose-Ward+transform">Penrose-Ward transform</a> relating <a class="existingWikiWord" href="/nlab/show/twistor+space">twistor space</a> to <a class="existingWikiWord" href="/nlab/show/Minkowski+spacetime">Minkowski spacetime</a>, on its generalization to <a class="existingWikiWord" href="/nlab/show/superalgebra">superalgebra</a> and <a class="existingWikiWord" href="/nlab/show/supergeometry">supergeometry</a>, and on applications to <a class="existingWikiWord" href="/nlab/show/super+Yang-Mills+theory">super Yang-Mills theory</a> and <a class="existingWikiWord" href="/nlab/show/supergravity">supergravity</a>:</p> <ul> <li><a class="existingWikiWord" href="/nlab/show/Yuri+Manin">Yuri Manin</a>, <em><a class="existingWikiWord" href="/nlab/show/Gauge+Field+Theory+and+Complex+Geometry">Gauge Field Theory and Complex Geometry</a></em>, Grundlehren der Mathematischen Wissenschaften <strong>289</strong>, Springer (1988) [<a href="https://doi.org/10.1007/978-3-662-07386-5">doi:10.1007/978-3-662-07386-5</a>]</li> </ul> <p>Introducing <a class="existingWikiWord" href="/nlab/show/quantum+linear+groups">quantum linear groups</a> as universal co-acting bialgebras (and their quotient <a class="existingWikiWord" href="/nlab/show/Hopf+algebras">Hopf algebras</a>):</p> <ul> <li><a class="existingWikiWord" href="/nlab/show/Yuri+I.+Manin">Yuri I. Manin</a>, <em>Quantum groups and non-commutative geometry</em>, CRM Short COurses, Springer (1988) [<a href="https://doi.org/10.1007/978-3-319-97987-8">doi:10.1007/978-3-319-97987-8</a>]</li> </ul> <p>On <a class="existingWikiWord" href="/nlab/show/quantum+cohomology">quantum cohomology</a> and <a class="existingWikiWord" href="/nlab/show/Gromov-Witten+invariants">Gromov-Witten invariants</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/Maxim+Kontsevich">Maxim Kontsevich</a>, <a class="existingWikiWord" href="/nlab/show/Yuri+Manin">Yuri Manin</a>, <em>Gromov-Witten classes, quantum cohomology, and enumerative geometry</em>, Commun. Math. Physics <strong>164</strong> (1994) 525-562 <a href="https://doi.org/10.1007/BF02101490">doi</a> arXiv:<a href="https://arxiv.org/pdf/hep-th/9402147">hep-th/9402147</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Yuri+Manin">Yuri Manin</a>, <em>Frobenius manifolds, quantum cohomology, and moduli spaces</em>, Amer. Math. Soc. Colloqium Publications <strong>47</strong>, 1999</p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Maxim+Kontsevich">Maxim Kontsevich</a>, <a class="existingWikiWord" href="/nlab/show/Yuri+Manin">Yuri Manin</a>, <a class="existingWikiWord" href="/nlab/show/Ralph+Kaufmann">Ralph Kaufmann</a>, <em>Quantum cohomology of a product</em>, Invent. Math. <strong>124</strong> (1996) 313-339 <a href="https://doi.org/10.1007/s002220050055">doi</a> arXiv:<a href="https://arxiv.org/abs/q-alg/9502009">q-alg/9502009</a></p> </li> </ul> <p>On <a class="existingWikiWord" href="/nlab/show/homological+algebra">homological algebra</a> and <a class="existingWikiWord" href="/nlab/show/homotopical+algebra">homotopical algebra</a> (via <a class="existingWikiWord" href="/nlab/show/triangulated+categories">triangulated categories</a> and including the <a class="existingWikiWord" href="/nlab/show/model+structure+on+dgc-algebras">model structure on dgc-algebras</a> for <a class="existingWikiWord" href="/nlab/show/rational+homotopy+theory">rational homotopy theory</a>):</p> <ul> <li><a class="existingWikiWord" href="/nlab/show/Sergei+Gelfand">Sergei Gelfand</a>, <a class="existingWikiWord" href="/nlab/show/Yuri+Manin">Yuri Manin</a>, <em><a class="existingWikiWord" href="/nlab/show/Methods+of+homological+algebra">Methods of homological algebra</a></em>, transl. from the 1988 Russian (Nauka Publ.) original, Springer 1996. xviii+372 pp. 2nd corrected ed. 2002 (<a href="https://doi.org/10.1007/978-3-662-12492-5">doi:10.1007/978-3-662-12492-5</a>)</li> </ul> <p>On <a class="existingWikiWord" href="/nlab/show/Frobenius+manifolds">Frobenius manifolds</a> and <a class="existingWikiWord" href="/nlab/show/quantum+cohomology">quantum cohomology</a>:</p> <ul> <li><a class="existingWikiWord" href="/nlab/show/Yuri+Manin">Yuri Manin</a>: <em>Frobenius manifolds, quantum cohomology, and moduli spaces</em>, Colloqium Publications <strong>47</strong>, Amer. Math. Soc. (1999) [<a href="https://bookstore.ams.org/coll-47">ams:</a>]</li> </ul> <p>and generalized to Frobenius <a class="existingWikiWord" href="/nlab/show/supermanifolds">supermanifolds</a> in <a class="existingWikiWord" href="/nlab/show/supergeometry">supergeometry</a>:</p> <ul> <li><a class="existingWikiWord" href="/nlab/show/Yuri+I.+Manin">Yuri I. Manin</a>, <a class="existingWikiWord" href="/nlab/show/Sergei+A.+Merkulov">Sergei A. Merkulov</a>: <em>Semisimple Frobenius (super)manifolds and quantum cohomology of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><msup><mi>P</mi> <mi>r</mi></msup></mrow><annotation encoding="application/x-tex">P^r</annotation></semantics></math></em>, Topol. Methods in Nonlinear Analysis <strong>9</strong> (1997) 107-161 [<a href="https://arxiv.org/abs/alg-geom/9702014">arXiv:alg-geom/9702014</a>, <a href="http://dx.doi.org/10.12775/TMNA.1997.006">doi:10.12775/TMNA.1997.006</a>]</li> </ul> <p>On relations of <a class="existingWikiWord" href="/nlab/show/AdS3%2FCFT2">AdS3/CFT2</a> to <a class="existingWikiWord" href="/nlab/show/hyperbolic+geometry">hyperbolic geometry</a> and <a class="existingWikiWord" href="/nlab/show/Arakelov+geometry">Arakelov geometry</a> of <a class="existingWikiWord" href="/nlab/show/algebraic+curves">algebraic curves</a>:</p> <ul> <li><a class="existingWikiWord" href="/nlab/show/Yuri+Manin">Yuri Manin</a>, <a class="existingWikiWord" href="/nlab/show/Matilde+Marcolli">Matilde Marcolli</a>, <em>Holography principle and arithmetic of algebraic curves</em>, Adv. Theor. Math. Phys. 5 (2002) 617-650 (<a href="https://arxiv.org/abs/hep-th/0201036">arXiv:hep-th/0201036</a></li> </ul> <p>On doubly <a class="existingWikiWord" href="/nlab/show/monoidal+categories">monoidal categories</a> and <a class="existingWikiWord" href="/nlab/show/quadratic+operads">quadratic operads</a>:</p> <ul> <li><a class="existingWikiWord" href="/nlab/show/Yuri+Ivanovich+Manin">Yuri Ivanovich Manin</a>, <a class="existingWikiWord" href="/nlab/show/Bruno+Vallette">Bruno Vallette</a>, <em>Monoidal structures on the categories of quadratic data</em>, Documenta Mathematica <strong>25</strong> (2020) 1727-1786 [<a href="https://arxiv.org/abs/1902.03778">arXiv:1902.03778</a>]</li> </ul> <h2 id="quotes">Quotes</h2> <blockquote> <p><em>What binds us to space-time is our rest mass, which prevents us from flying at the speed of light, when time stops and space loses meaning. In a world of light there are neither points nor moments of time; beings woven from light would live “nowhere” and “nowhen”; only poetry and mathematics are capable of speaking meaningfully about such things</em></p> </blockquote> <p><em>Mathematics as Metaphor</em>: Selected Essays of Yuri I. Manin (ed. 2007) (<a href="https://libquotes.com/yuri-manin/quote/lbj0h0e">libquotes</a>)</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 September 12, 2024 at 10:15:37. 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