{"id":5878,"date":"2025-02-11T09:27:05","date_gmt":"2025-02-11T08:27:05","guid":{"rendered":"https:\/\/uni-freiburg.de\/frias\/?p=5878"},"modified":"2025-02-11T09:27:05","modified_gmt":"2025-02-11T08:27:05","slug":"prof-dr-joseph-bernstein","status":"publish","type":"post","link":"https:\/\/uni-freiburg.de\/frias\/prof-dr-joseph-bernstein\/","title":{"rendered":"Prof. Dr. Joseph Bernstein"},"content":{"rendered":"\n<div class=\"wp-block-group has-global-padding is-layout-constrained wp-block-group-is-layout-constrained\">\n<div style=\"height:25px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-columns are-vertically-aligned-top is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-vertically-aligned-top is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66.66%\">\n<div class=\"wp-block-media-text is-stacked-on-mobile is-vertically-aligned-top\" style=\"grid-template-columns:40% auto\"><figure class=\"wp-block-media-text__media\"><img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"200\" src=\"https:\/\/uni-freiburg.de\/frias\/wp-content\/uploads\/sites\/62\/BernsteinJoseph.jpg\" alt=\"Portrait of Joseph Bernstein\" class=\"wp-image-5879 size-full\" \/><\/figure><div class=\"wp-block-media-text__content\">\n<p>Tel Aviv University<br>Algebraic Geometry<br><br>External Senior Fellow<br>June &#8211; August 2018<\/p>\n\n\n\n<div class=\"is-layout-flex wp-block-ufr-buttons-is-layout-flex\">\n\t<\/div>\n\n\n\n\n<p>E-Mail: <a href=\"mailto:bernstein@post.tau.ac.il\">bernstein@post.tau.ac.il<\/a><\/p>\n<\/div><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-top is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33.33%\">\n<div class=\"[&amp;amp;&amp;gt;*]:bl-relative last:[&amp;amp;&amp;gt;*.bl-absolute]:bl-absolute\n\t\t\t[&amp;amp;&amp;gt;*]:bl-z-20 last:[&amp;amp;&amp;gt;*]:bl-z-10 bl-relative bl-overflow-x-clip\n\t\t\t[.wp-block-ufr-section_&amp;amp;]:bl-overflow-x-visible\n\t\t\tbl-bg-identity-lightblue bl-text-identity-black dark:bl-bg-identity-lightblue dark:bl-text-identity-black bl-py-[24px]  align wp-block-ufr-section has-global-padding is-layout-constrained wp-block-ufr-section-is-layout-constrained\">\n\n\t\n\n<p>Last Update: 31.08.2018<\/p>\n\n\t<\/div>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66.66%\">\n<h2 class=\"wp-block-heading\">Curriculum Vitae<\/h2>\n\n\n\n<p><strong>Education<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>1968 &#8211; 1972 Ph.D., Dept. of Mathematics, Moscow State University<\/li>\n\n\n\n<li>1963 &#8211; 1968 M.Sc., Dept. of Mathematics, Moscow State University<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Academic and Professional Experience<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>October 2014 &#8211; present Professor Emeritus, School of Mathematical Sciences, Tel Aviv University, Israel<\/li>\n\n\n\n<li>September 1993 \u2013 September 2014 Professor, School of Mathematical Sciences, Tel Aviv University, Israel<\/li>\n\n\n\n<li>January 1983 &#8211; August 1993 Professor, Department of Mathematics, Harvard University, USA<\/li>\n\n\n\n<li>1971 &#8211; 1978 Junior Researcher, Laboratory of Mathematical Methods in Biology, Moscow State University, USSR<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Long term visiting positions<\/h4>\n\n\n\n<p>May &#8211; August 1981 Member, IHES Bures-sur-Yvette, France<\/p>\n\n\n\n<p>July &#8211; December 2013 Member, Max Planck Institute for Mathematics, Bonn, Germany<\/p>\n\n\n\n<p>September &#8211; December 2010 Member, Institute for Advance Studies, Hebrew University, Israel<\/p>\n\n\n\n<p>September &#8211; December 2004 Visiting Professor, Courant Institute, New York University, USA<\/p>\n\n\n\n<p>September &#8211; December 2001 Visiting Professor, Department of Mathematics, University of California, Berkeley, USA<\/p>\n\n\n\n<p>October 1991 &#8211; June 1992 Visiting Professor, Department of Mathematics, Tel Aviv University, Israel<\/p>\n\n\n\n<p>October 1987 &#8211; July 1988 Member, Institute for Advance Studies, Hebrew University, Israe<\/p>\n\n\n\n<p>September &#8211; December 1985 Member, Institute for Advance Studies, Princeton, USA<\/p>\n\n\n\n<p>August 1981 &#8211; December 1982 Visiting Professor, Department of Mathematics, University of Maryland, USA<\/p>\n\n\n\n<div style=\"height:32px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"bl-w-full wp-block-ufr-accordion\">\n\n\n<article class=\"ufr-accordion-container-wrapper\" data-accordion=\"animationDuration: 400; direction: vertical; collapsible: true; \">\n\t<div class=\"ufr-accordion-container-flex-wrapper \">\n\t\t\n\n<section\n\tid=\"Selected-Publications\"\n\tclass=\"ufr-accordion-item-section\n\tufr-accordion-item-section--vertical\">\n\t<div class=\"bl-group\/accordion-header ufr-accordion-item-header\n\t\t\t\"\n\trole=\"button\"\n\ttabindex=\"0\"\n\taria-label=\"Toggle accordion item: Selected Publications\"\n\taria-controls=\"Accordion Selected-Publications content\"\n\t>\n\t\t<div class=\"ufr-accordion-item-header-wrapper\n\t\t\t\t\t\">\n\t\t\t\t\t\t<h3 class=\"ufr-accordion-item-header-heading\n\t\t\t\tufr-accordion-item-header-heading--vertical\t\t\t\">\n\t\t\t\tSelected Publications\t\t\t<\/h3>\n\t\t<\/div>\n\t\t<span class=\"\n\t\t\tchevron-container\n\t\t\tufr-accordion-item-header-chevron-container\n\t\t\tufr-accordion-item-header-chevron-container--!numbered ufr-accordion-header-chevron-container--light-in-lightmode ufr-accordion-header-chevron-container--dark-in-darkmode \t\t\" aria-hidden=\"true\">\n\t\t\t<svg width=\"100%\" viewBox=\"0 0 35 50\" fill=\"none\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"\n\taria-label=\"chevron-right\" class=\"bl-h-[40px] md:bl-h-[40px] xl:bl-h-[100px] bl-rotate-90\" role=\"img\">\n\t<title>chevron-right<\/title>\n\t<path d=\"M5.00012 5L25.6062 25.0002L5.00012 45\" stroke=\"currentColor\" stroke-width=\"12\" \/>\n<\/svg>\n\t\t<\/span>\n\t<\/div>\n\t<div\n\t\tid=\"Accordion Selected-Publications content\"\n\t\tclass=\"ufr-accordion-item-body\n\t\t\tufr-accordion-item-body--vertical\t\t\"\n\t\t\t>\n\t\t\t\t<div\n\t\tclass=\"ufr-accordion-item-body-outer-content-wrapper\n\t\t\t\t\t\"\n\t\taria-hidden=\"true\"\n\t\t>\n\t\t\t<div class=\"is-layout-flow\n\t\t\t\t\t\t\t\">\n\t\t\t\t\n\n<ul class=\"wp-block-list\">\n<li>J. Bernstein, A.V. Zelevinsky. Induced representations of GL(n) over p-adic field. Functional Analysis and its Applications 10, No.3, 74-75 (1976)<\/li>\n\n\n\n<li>J. Bernstein, A.A. Beilinson, P. Deligne. Faisceux pervers. Asterisque 100, 3-171 (1983)<\/li>\n\n\n\n<li>J. Bernstein, Representations of p-adic groups. Lectures by Joseph Bernstein. Written by Karl E. Rumelhart. Harvard University. (Fall 1992).<\/li>\n\n\n\n<li>J. Bernstein, A. Reznikov. Subconvexity bounds for triple L-functions and Representation Theory, Annals of Mathematics, no. 172 (2010), 1679-1718.<\/li>\n\n\n\n<li>J. Bernstein Stacks in Representation Theory. arXiv:1410.0435v3 <a href=\"\"><\/a>[math.RT] 12 May 2016<\/li>\n<\/ul>\n\n\t\t\t<\/div>\n\t\t<\/div>\n\t<\/div>\n<\/section>\n\n\n\n<section\n\tid=\"FRIAS-Project-2\"\n\tclass=\"ufr-accordion-item-section\n\tufr-accordion-item-section--vertical\">\n\t<div class=\"bl-group\/accordion-header ufr-accordion-item-header\n\t\t\t\"\n\trole=\"button\"\n\ttabindex=\"0\"\n\taria-label=\"Toggle accordion item: FRIAS Project\"\n\taria-controls=\"Accordion FRIAS-Project-2 content\"\n\t>\n\t\t<div class=\"ufr-accordion-item-header-wrapper\n\t\t\t\t\t\">\n\t\t\t\t\t\t<h3 class=\"ufr-accordion-item-header-heading\n\t\t\t\tufr-accordion-item-header-heading--vertical\t\t\t\">\n\t\t\t\tFRIAS Project\t\t\t<\/h3>\n\t\t<\/div>\n\t\t<span class=\"\n\t\t\tchevron-container\n\t\t\tufr-accordion-item-header-chevron-container\n\t\t\tufr-accordion-item-header-chevron-container--!numbered ufr-accordion-header-chevron-container--light-in-lightmode ufr-accordion-header-chevron-container--dark-in-darkmode \t\t\" aria-hidden=\"true\">\n\t\t\t<svg width=\"100%\" viewBox=\"0 0 35 50\" fill=\"none\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"\n\taria-label=\"chevron-right\" class=\"bl-h-[40px] md:bl-h-[40px] xl:bl-h-[100px] bl-rotate-90\" role=\"img\">\n\t<title>chevron-right<\/title>\n\t<path d=\"M5.00012 5L25.6062 25.0002L5.00012 45\" stroke=\"currentColor\" stroke-width=\"12\" \/>\n<\/svg>\n\t\t<\/span>\n\t<\/div>\n\t<div\n\t\tid=\"Accordion FRIAS-Project-2 content\"\n\t\tclass=\"ufr-accordion-item-body\n\t\t\tufr-accordion-item-body--vertical\t\t\"\n\t\t\t>\n\t\t\t\t<div\n\t\tclass=\"ufr-accordion-item-body-outer-content-wrapper\n\t\t\t\t\t\"\n\t\taria-hidden=\"true\"\n\t\t>\n\t\t\t<div class=\"is-layout-flow\n\t\t\t\t\t\t\t\">\n\t\t\t\t\n\n<h3 class=\"wp-block-heading\"><strong><strong>Soergel&#8217;s conjecture and Langlands\u2019 correspondence for p-adic groups<\/strong><\/strong>.<\/h3>\n\n\n\n<p>Program: Cohomology in Algebraic Geometry and Representation Theory.<\/p>\n\n\n\n<p>During my stay at FRIAS I am planning to work on the following interrelated projects.<\/p>\n\n\n\n<p><strong>1.<\/strong> My main point of interest are Soergel&#8217;s conjectures on representations of real and<em> p<\/em>-adic groups. Let <em>M<\/em>(<em>G<\/em>) be the category of representations of some group <em>G<\/em>. Usually we consider some finite direct summand <em>M <\/em>of this category. Soergel&#8217;s conjectures describe the structure of this category in terms of the Langlands&#8217; dual group <em>G.<\/em><\/p>\n\n\n\n<p>(i) One of the main features of these conjectures is an idea that behind the category<em> M <\/em>there is a graded category <em>N <\/em>that is Koszul; the Koszul dual of this category can be expressed in terms of the dual group <em>G. <\/em>I have worked out some examples that convinced me that probably this category <em>N <\/em>in fact should be filtered, not graded. I have some ideas how to construct this category for a real group <em>G<\/em>. I will try to work out this construction and generalize it to include <em>p<\/em>-adic groups.<\/p>\n\n\n\n<p>(ii) In case of <em>p<\/em>-adic groups one can consider the category <em>M <\/em>corresponding to the principal block. It can be described in terms of the affine Hecke algebra <em>H<\/em>. Algebra <em>H <\/em>has natural _ltration. Lusztig has introduced a graded version of this algebra <em>H<\/em><em>g<\/em>. He also showed that categories of representations of algebras <em>H <\/em>and <em>H<\/em><em>g <\/em>are equivalent. So probably in Soergel&#8217;s conjectures we have both _ltered category and graded category. It would be extremely interesting to understand these structures in this case and also in general situation.<\/p>\n\n\n\n<p>(iii) Recently I realized that the notion of Langlands dual group should be slightly modifed. It would be important to use this new construction in precise formulation of Soergel&#8217;s conjectures.<\/p>\n\n\n\n<p><strong>2.<\/strong> The Koszul duality that appears in Soergel&#8217;s conjectures has many different applications. For me the most interesting are its applications to Grothendieck duality theory in Algebraic Geometry. I am planning to discuss the Koszul duality and its applications in Algebraic Geometry with Professor Soergel.<\/p>\n\n\t\t\t<\/div>\n\t\t<\/div>\n\t<\/div>\n<\/section>\n\n\t<\/div>\n<\/article>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33.33%\">\n<div class=\"[&amp;amp;&amp;gt;*]:bl-relative last:[&amp;amp;&amp;gt;*.bl-absolute]:bl-absolute\n\t\t\t[&amp;amp;&amp;gt;*]:bl-z-20 last:[&amp;amp;&amp;gt;*]:bl-z-10 bl-relative bl-overflow-x-clip\n\t\t\t[.wp-block-ufr-section_&amp;amp;]:bl-overflow-x-visible\n\t\t\tbl-bg-transparent bl-text-inherit dark:bl-bg-transparent dark:bl-text-inherit  alignfull wp-block-ufr-section has-global-padding is-layout-constrained wp-block-ufr-section-is-layout-constrained\">\n\n\t\t\t\t<div class=\"bl-absolute bl-inset-0 bl-w-full bl-h-full bl-pointer-events-none bl-mt-0\">\n\t\t\t<div\n\t\t\tclass=\"bl-absolute bl-origin-center\n\t\t\t\tbl-w-96\t\t\t\tbl-top-[50%] -bl-translate-y-[50%] bl-left-[50%] -bl-translate-x-[50%]\t\t\t\t\">\n\t\t\t\t<svg\n\twidth=\"100%\"\n\tviewBox=\"0 0 64.5 64.5\"\n\tfill=\"none\"\n\txmlns=\"http:\/\/www.w3.org\/2000\/svg\"\n\taria-label=\"\"\n\tclass=\"bl-relative bl-block dark:bl-hidden bl-w-full\"\n\trole=\"img\">\n\t<title><\/title>\n<linearGradient\n\tid=\"kze6t1SNQo\"\n\tx1=\"50%\" y1=\"100%\"\n\tx2=\"50%\" y2=\"0%\">\n\t<stop\n\t\toffset=\"0%\"\n\t\tstop-color=\"#f5c2ed\"\n\t\tstop-opacity=\"1\" \/>\n\t<stop\n\t\toffset=\"100%\"\n\t\tstop-color=\"#f5c2ed\"\n\t\tstop-opacity=\"0\" \/>\n<\/linearGradient>\n\t<path\n\t\td=\"m32.25,64c17.53,0,31.75-14.21,31.75-31.75S49.78.5,32.25.5.5,14.71.5,32.25s14.21,31.75,31.75,31.75\"\n\t\tstroke-width=\"2px\"\n\t\tvector-effect=\"non-scaling-stroke\"\n\t\tfill=\"url(#kze6t1SNQo)\" \/>\n<\/svg>\n<svg\n\twidth=\"100%\"\n\tviewBox=\"0 0 64.5 64.5\"\n\tfill=\"none\"\n\txmlns=\"http:\/\/www.w3.org\/2000\/svg\"\n\taria-label=\"\"\n\tclass=\"bl-relative bl-hidden dark:bl-block bl-w-full\"\n\trole=\"img\">\n\t<title><\/title>\n<linearGradient\n\tid=\"P1I5pHLfFO\"\n\tx1=\"50%\" y1=\"100%\"\n\tx2=\"50%\" y2=\"0%\">\n\t<stop\n\t\toffset=\"0%\"\n\t\tstop-color=\"#000149\"\n\t\tstop-opacity=\"1\" \/>\n\t<stop\n\t\toffset=\"100%\"\n\t\tstop-color=\"#000149\"\n\t\tstop-opacity=\"0\" \/>\n<\/linearGradient>\n\t<path\n\t\td=\"m32.25,64c17.53,0,31.75-14.21,31.75-31.75S49.78.5,32.25.5.5,14.71.5,32.25s14.21,31.75,31.75,31.75\"\n\t\tstroke-width=\"2px\"\n\t\tvector-effect=\"non-scaling-stroke\"\n\t\tfill=\"url(#P1I5pHLfFO)\" \/>\n<\/svg>\n\t\t\t<\/div>\n\t\t<\/div>\n\t\t<\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:128px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Tel Aviv UniversityAlgebraic Geometry External Senior FellowJune &#8211; August 2018 E-Mail: bernstein@post.tau.ac.il Curriculum Vitae Education Academic and Professional Experience Long term visiting positions May &#8211; August 1981 Member, IHES Bures-sur-Yvette, France July &#8211; December 2013 Member, Max Planck Institute for Mathematics, Bonn, Germany September &#8211; December 2010 Member, Institute for Advance Studies, Hebrew University, Israel<\/p>\n","protected":false},"author":389,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_trash_the_other_posts":false,"editor_notices":[],"_show_in_pageentry_slider":true,"_pageentry_slider_title":"","footnotes":""},"categories":[54,26,67,159,42,294],"tags":[],"class_list":["post-5878","post","type-post","status-publish","format-standard","hentry","category-2017-18","category-fellow","category-israel","category-mathematics","category-senior-fellowship-programme","category-tel-aviv-university"],"featured_image_url":null,"featured_image_alt":"","_links":{"self":[{"href":"https:\/\/uni-freiburg.de\/frias\/wp-json\/wp\/v2\/posts\/5878","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/uni-freiburg.de\/frias\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/uni-freiburg.de\/frias\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/uni-freiburg.de\/frias\/wp-json\/wp\/v2\/users\/389"}],"replies":[{"embeddable":true,"href":"https:\/\/uni-freiburg.de\/frias\/wp-json\/wp\/v2\/comments?post=5878"}],"version-history":[{"count":1,"href":"https:\/\/uni-freiburg.de\/frias\/wp-json\/wp\/v2\/posts\/5878\/revisions"}],"predecessor-version":[{"id":5880,"href":"https:\/\/uni-freiburg.de\/frias\/wp-json\/wp\/v2\/posts\/5878\/revisions\/5880"}],"wp:attachment":[{"href":"https:\/\/uni-freiburg.de\/frias\/wp-json\/wp\/v2\/media?parent=5878"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/uni-freiburg.de\/frias\/wp-json\/wp\/v2\/categories?post=5878"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/uni-freiburg.de\/frias\/wp-json\/wp\/v2\/tags?post=5878"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}