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Albert Schwarz - Wikipedia

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.mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">In this name that follows <a href="/wiki/Eastern_Slavic_naming_customs" title="Eastern Slavic naming customs">Eastern Slavic naming customs</a>, the <a href="/wiki/Patronymic" title="Patronymic">patronymic</a> is <i> Solomonovich</i>&#32;and the <a href="/wiki/Surname" title="Surname">family name</a> is <i> Schwarz</i>.</div> <p><b>Albert Solomonovich Schwarz</b><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> (<span class="rt-commentedText nowrap"><span class="IPA nopopups noexcerpt" lang="en-fonipa"><a href="/wiki/Help:IPA/English" title="Help:IPA/English">/<span style="border-bottom:1px dotted"><span title="/ʃ/: &#39;sh&#39; in &#39;shy&#39;">ʃ</span><span title="&#39;w&#39; in &#39;wind&#39;">w</span><span title="/ɔːr/: &#39;ar&#39; in &#39;war&#39;">ɔːr</span><span title="&#39;t&#39; in &#39;tie&#39;">t</span><span title="&#39;s&#39; in &#39;sigh&#39;">s</span></span>/</a></span></span> <a href="/wiki/Help:Pronunciation_respelling_key" title="Help:Pronunciation respelling key"><i title="English pronunciation respelling"><span style="font-size:90%">SHWORTS</span></i></a>; <a href="/wiki/Russian_language" title="Russian language">Russian</a>: <span lang="ru">Альберт Соломонович Шварц</span>; born June 24, 1934) is a Soviet and American mathematician and a theoretical physicist educated in the Soviet Union and now a professor at the <a href="/wiki/University_of_California,_Davis" title="University of California, Davis">University of California, Davis</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Early_life_and_education">Early life and education</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Albert_Schwarz&amp;action=edit&amp;section=1" title="Edit section: Early life and education"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Schwarz was born in <a href="/wiki/Kazan" title="Kazan">Kazan</a> to <a href="/wiki/Ashkenazi_Jewish" class="mw-redirect" title="Ashkenazi Jewish">Ashkenazi Jewish</a> parents, <a href="/wiki/Soviet_Union" title="Soviet Union">Soviet Union</a>. His parents were arrested in the <a href="/wiki/Stalinist_purges" class="mw-redirect" title="Stalinist purges">Stalinist purges</a> in 1937.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">&#91;</span>2<span class="cite-bracket">&#93;</span></a></sup> </p><p>Schwarz studied under <a href="/wiki/Vadim_Yefremovich" title="Vadim Yefremovich">Vadim Yefremovich</a> at Ivanovo Pedagogical Institute, having been denied admittance to <a href="/wiki/Moscow_State_University" title="Moscow State University">Moscow State University</a> on the grounds that he was the son of "<a href="/wiki/Enemies_of_the_people" class="mw-redirect" title="Enemies of the people">enemies of the people</a>."<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> </p> <div class="mw-heading mw-heading2"><h2 id="Career_and_later_life">Career and later life</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Albert_Schwarz&amp;action=edit&amp;section=2" title="Edit section: Career and later life"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>After defending his dissertation in 1958, he took a job at Voronezh University. In 1964 he was offered a job at <a href="/wiki/Moscow_Engineering_Physics_Institute" title="Moscow Engineering Physics Institute">Moscow Engineering Physics Institute</a>.<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> He immigrated to the United States in 1989.<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> </p> <div class="mw-heading mw-heading2"><h2 id="Contributions">Contributions</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Albert_Schwarz&amp;action=edit&amp;section=3" title="Edit section: Contributions"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Schwarz is one of the pioneers of <a href="/wiki/Morse_theory" title="Morse theory">Morse theory</a> and brought up the first example of a <a href="/wiki/Topological_quantum_field_theory" title="Topological quantum field theory">topological quantum field theory</a>.<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> The Schwarz genus, one of the fundamental notions of <a href="/wiki/Topological_complexity" title="Topological complexity">topological complexity</a>, is named after him.<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> Schwarz worked on some examples in <a href="/wiki/Noncommutative_geometry" title="Noncommutative geometry">noncommutative geometry</a>. He is the "S" in the <a href="/w/index.php?title=AKSZ_theory&amp;action=edit&amp;redlink=1" class="new" title="AKSZ theory (page does not exist)">AKSZ model</a> (named after Mikhail Alexandrov, <a href="/wiki/Maxim_Kontsevich" title="Maxim Kontsevich">Maxim Kontsevich</a>, Schwarz, and Oleg Zaboronski).<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> </p> <div class="mw-heading mw-heading2"><h2 id="Recognition">Recognition</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Albert_Schwarz&amp;action=edit&amp;section=4" title="Edit section: Recognition"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In 1990, Schwarz was an invited speaker of the <a href="/wiki/International_Congress_of_Mathematicians" title="International Congress of Mathematicians">International Congress of Mathematicians</a> in <a href="/wiki/Kyoto" title="Kyoto">Kyoto</a>. He was elected to the 2018 class of <a href="/wiki/Fellow" title="Fellow">fellows</a> of the <a href="/wiki/American_Mathematical_Society" title="American Mathematical Society">American Mathematical Society</a>.<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> <div class="mw-heading mw-heading2"><h2 id="Monographs">Monographs</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Albert_Schwarz&amp;action=edit&amp;section=5" title="Edit section: Monographs"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><i>Topology for physicists</i>, Springer, 1996.</li> <li><i>Quantum field theory and topology</i>, Grundlehren der Math. Wissen. 307, Springer 1993 (translated from Russian original <i>Kvantovaja teorija polja i topologija, Nauka</i>, Moscow, 1989).</li> <li>A. S. Švarc, <i>Математические основы квантовой теории поля (Mathematical aspects of quantum field theory)</i>, Atomizdat, Moscow, 1975.</li> <li><i>Mathematical Foundations of Quantum Field Theory</i>, 2020.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Papers_(selection)"><span id="Papers_.28selection.29"></span>Papers (selection)</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Albert_Schwarz&amp;action=edit&amp;section=6" title="Edit section: Papers (selection)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>A. S. Švarc, A volume invariant of coverings <span class="languageicon">(in Russian)</span>, <a href="/wiki/Doklady_Akademii_Nauk_SSSR" class="mw-redirect" title="Doklady Akademii Nauk SSSR">Doklady Akademii Nauk SSSR</a>, <b>105</b> (1955), pp.&#160;32–34.</li> <li>A. S. Švarc, Род расслоенного пространства, <i>Докл</i>. <i>АН СССР</i> (The genus of a fiber space (Russian), <a href="/wiki/Doklady_Akademii_Nauk_SSSR" class="mw-redirect" title="Doklady Akademii Nauk SSSR">Doklady Akademii Nauk SSSR</a> <b>119</b> (1958), no. 2, 219–222.</li> <li>A. Schwarz, O. Zaboronsky, Supersymmetry and localization, <i>Comm. Math. Phys.</i> <b>183</b>(2) (1997), 463–476.</li> <li>M. Alexandrov, M. Kontsevich, A. Schwarz, O. Zaboronsky, The geometry of the master equation and topological quantum field theory, <i>Int. J. Modern Phys</i>. <b>A12</b>(7):1405–1429, 1997.</li> <li>V. Kac, A. Schwarz, Geometric interpretation of the partition function of 2D gravity, <i>Phys. Lett.</i> <b>B257</b> (1991), nos. 3–4, 329–334.</li> <li>A. A. Belavin, A. M. Polyakov, A. S. Schwartz, Yu. S. Tyupkin, Pseudoparticle solutions of the Yang-Mills equations, <i>Phys. Lett.</i> <b>B59</b> (1975), no. 1, 85–87.</li> <li>V. N. Romanov, A. S. Švarc, Anomalies and elliptic operators (Russian), <i>Teoret. Mat. Fiz.</i> <b>41</b> (1979), no. 2, 190–204.</li> <li>S. N. Dolgikh, A. A. Rosly, A. S. Schwarz, Supermoduli spaces, <i>Comm. Math. Phys.</i> <b>135</b> (1990), no. 1, 91–100.</li></ul> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Albert_Schwarz&amp;action=edit&amp;section=7" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/ADHM_construction" title="ADHM construction">ADHM construction</a></li> <li><a href="/wiki/BPST_instanton" title="BPST instanton">BPST instanton</a></li> <li><a href="/wiki/Instanton" title="Instanton">Instanton</a></li> <li><a href="/wiki/Chern%E2%80%93Simons_theory" title="Chern–Simons theory">Chern–Simons theory</a></li> <li><a href="/wiki/Schwarz-type_TQFTs" class="mw-redirect" title="Schwarz-type TQFTs">Schwarz-type TQFTs</a></li> <li><a href="/wiki/%C5%A0varc%E2%80%93Milnor_lemma" title="Švarc–Milnor lemma">Švarc–Milnor lemma</a></li> <li><a href="/wiki/Supermanifold" title="Supermanifold">Supermanifold</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Albert_Schwarz&amp;action=edit&amp;section=8" title="Edit section: Notes"><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"><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">Credited as <i>Schwartz</i> in A. A. Belavin <i>et al</i> (1975).</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></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="https://www.math.ucdavis.edu/~schwarz/bion.pdf">"My life in science"</a> <span class="cs1-format">(PDF)</span>. <i>ucdavis.edu</i><span class="reference-accessdate">. Retrieved <span class="nowrap">18 May</span> 2023</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=ucdavis.edu&amp;rft.atitle=My+life+in+science&amp;rft_id=https%3A%2F%2Fwww.math.ucdavis.edu%2F~schwarz%2Fbion.pdf&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AAlbert+Schwarz" 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 class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.genealogy.math.ndsu.nodak.edu/id.php?id=12690">"Albert Schwarz"</a>. <i>The Mathematics Genealogy Project</i><span class="reference-accessdate">. Retrieved <span class="nowrap">18 May</span> 2023</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=The+Mathematics+Genealogy+Project&amp;rft.atitle=Albert+Schwarz&amp;rft_id=https%3A%2F%2Fwww.genealogy.math.ndsu.nodak.edu%2Fid.php%3Fid%3D12690&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AAlbert+Schwarz" 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 class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.ias.edu/ideas/2011/witten-knots-quantum-theory">"Knots and Quantum Theory - Ideas &#124; Institute for Advanced Study"</a>. 5 August 2011.</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=Knots+and+Quantum+Theory+-+Ideas+%26%23124%3B+Institute+for+Advanced+Study&amp;rft.date=2011-08-05&amp;rft_id=https%3A%2F%2Fwww.ias.edu%2Fideas%2F2011%2Fwitten-knots-quantum-theory&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AAlbert+Schwarz" 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="CITEREFSchwarz2020" class="citation book cs1">Schwarz, Albert (2020). <i>Mathematical Foundations of Quantum Field Theory</i>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a>&#160;<a href="/wiki/Special:BookSources/978-9813278639" title="Special:BookSources/978-9813278639"><bdi>978-9813278639</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&amp;rft.genre=book&amp;rft.btitle=Mathematical+Foundations+of+Quantum+Field+Theory&amp;rft.date=2020&amp;rft.isbn=978-9813278639&amp;rft.aulast=Schwarz&amp;rft.aufirst=Albert&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AAlbert+Schwarz" 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 class="citation web cs1"><a rel="nofollow" class="external text" href="https://ncatlab.org/nlab/show/Albert+Schwarz">"Albert Schwarz in nLab"</a>.</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=Albert+Schwarz+in+nLab&amp;rft_id=https%3A%2F%2Fncatlab.org%2Fnlab%2Fshow%2FAlbert%2BSchwarz&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AAlbert+Schwarz" 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="CITEREFVassiliev2011" class="citation journal cs1">Vassiliev, V. A. (2011). "Topological complexity and Schwarz genus of general real polynomial equation". <i>Moscow Mathematical Journal</i>. <b>11</b> (3): 617–625, 632. <a href="/wiki/MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a>&#160;<a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=2894434">2894434</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=Moscow+Mathematical+Journal&amp;rft.atitle=Topological+complexity+and+Schwarz+genus+of+general+real+polynomial+equation&amp;rft.volume=11&amp;rft.issue=3&amp;rft.pages=617-625%2C+632&amp;rft.date=2011&amp;rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D2894434%23id-name%3DMR&amp;rft.aulast=Vassiliev&amp;rft.aufirst=V.+A.&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AAlbert+Schwarz" 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="CITEREFCattaneoFelder2001" class="citation journal cs1">Cattaneo, Alberto S.; Felder, Giovanni (2001). "On the AKSZ formulation of the Poisson sigma model". <i>Letters in Mathematical Physics</i>. <b>56</b> (2): 163–179. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1023%2FA%3A1010963926853">10.1023/A:1010963926853</a>. <a href="/wiki/MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a>&#160;<a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=1854134">1854134</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=Letters+in+Mathematical+Physics&amp;rft.atitle=On+the+AKSZ+formulation+of+the+Poisson+sigma+model&amp;rft.volume=56&amp;rft.issue=2&amp;rft.pages=163-179&amp;rft.date=2001&amp;rft_id=info%3Adoi%2F10.1023%2FA%3A1010963926853&amp;rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D1854134%23id-name%3DMR&amp;rft.aulast=Cattaneo&amp;rft.aufirst=Alberto+S.&amp;rft.au=Felder%2C+Giovanni&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AAlbert+Schwarz" 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 class="citation cs2"><a rel="nofollow" class="external text" href="http://ams.org/profession/ams-fellows/new-fellows"><i>2018 Class of the Fellows of the AMS</i></a>, <a href="/wiki/American_Mathematical_Society" title="American Mathematical Society">American Mathematical Society</a><span class="reference-accessdate">, retrieved <span class="nowrap">2017-11-03</span></span></cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&amp;rft.genre=book&amp;rft.btitle=2018+Class+of+the+Fellows+of+the+AMS&amp;rft.pub=American+Mathematical+Society&amp;rft_id=http%3A%2F%2Fams.org%2Fprofession%2Fams-fellows%2Fnew-fellows&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AAlbert+Schwarz" class="Z3988"></span></span> </li> </ol></div></div> <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=Albert_Schwarz&amp;action=edit&amp;section=9" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="https://mathgenealogy.org/id.php?id=12690">Albert Schwarz</a> at the <a href="/wiki/Mathematics_Genealogy_Project" title="Mathematics Genealogy Project">Mathematics Genealogy Project</a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20101125124406/http://www.math.ucdavis.edu/~schwarz/">Biography at ucdavis.edu</a></li> <li>Шварц Альберт Соломонович // Воронежская энциклопедия&#160;: в 2 т. / Гл. ред. М. Д. Карпачёв. — Воронеж&#160;: Центр духовного возрождения Чернозёмного края, 2008. — Т. 2&#160;: Н — Я. — 524 с.&#160;: ил., карты.</li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist 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