{"id":2308,"date":"2022-03-02T13:31:49","date_gmt":"2022-03-02T11:31:49","guid":{"rendered":"https:\/\/mathematics.haifa.ac.il\/?p=2308"},"modified":"2022-03-09T16:31:59","modified_gmt":"2022-03-09T14:31:59","slug":"colloquium-tuesday-march-8-2022-speaker-jurij-volcic-university-of-copenhagen-title-determinantal-zeros-of-noncommutative-polynomials","status":"publish","type":"post","link":"https:\/\/mathematics.haifa.ac.il\/?p=2308","title":{"rendered":"Colloquium: Tuesday, March 8, 2022. Speaker:  Jurij Volcic (University of Copenhagen). Title: &#8220;Determinantal zeros of noncommutative polynomials&#8221;."},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">The zoom link for our meetings is:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/us02web.zoom.us\/j\/83337601824\">https:\/\/us02web.zoom.us\/j\/83337601824<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Time:&nbsp;<strong>14:00<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Abstract:&nbsp;&nbsp;Hilbert&#8217;s Nullstellensatz on zero sets of polynomials is one of the most fundamental correspondences between algebra and geometry.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In recent years, there has been an emerging interest in polynomial equations and inequalities in several matrix variables, prompted by developments in control theory, quantum information, operator algebras and polynomial optimization.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The arising problems call for a suitable version of (real) algebraic geometry in noncommuting variables.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This talk concerns a Nullstellensatz fitting this context.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Given a noncommutative polynomial f (an element of a free algebra), its free locus is the collection of matrix tuples X such that f(X) is a singular matrix. This is a noncommutative analog of a hypersurface in algebraic geometry. The main results of the talk are the correspondence between components of the free locus of f and irreducible factors of f, and a Nullstellensatz for free loci: a noncommutative polynomial g attains singular values wherever f attains singular values if and only if irreducible factors of f are essentially factors of g. Several applications for noncommutative polynomial inequalities will also be discussed.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The zoom link for our meetings is: https:\/\/us02web.zoom.us\/j\/83337601824 Time:&nbsp;14:00 Abstract:&nbsp;&nbsp;Hilbert&#8217;s Nullstellensatz on zero sets of polynomials is one of the most fundamental correspondences between algebra and geometry. In recent years, there has been an emerging interest in polynomial equations and&#8230;<br \/><a class=\"read-more-button\" href=\"https:\/\/mathematics.haifa.ac.il\/?p=2308\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[],"class_list":["post-2308","post","type-post","status-publish","format-standard","hentry","category-colloquium"],"_links":{"self":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/2308","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2308"}],"version-history":[{"count":1,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/2308\/revisions"}],"predecessor-version":[{"id":2309,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/2308\/revisions\/2309"}],"wp:attachment":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2308"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2308"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2308"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}