{"id":2062,"date":"2020-09-29T07:34:03","date_gmt":"2020-09-29T14:34:03","guid":{"rendered":"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&#038;p=2062"},"modified":"2020-09-29T07:35:05","modified_gmt":"2020-09-29T14:35:05","slug":"prof-grigoriy-blekherman","status":"publish","type":"tribe_events","link":"https:\/\/colleges.claremont.edu\/ccms\/event\/prof-grigoriy-blekherman\/","title":{"rendered":"Prof. Grigoriy Blekherman"},"content":{"rendered":"<p><strong>Title:<\/strong> Nonnegative Polynomials and Sums of Squares<\/p>\n<p><strong>Abstract:<\/strong> Is <em>x<sup>4<\/sup>-2x<sup>3<\/sup>+7x<sup>2<\/sup>-2x+1<\/em> nonnegative for any value of <em>x<\/em>? One way of showing that this holds is by writing <em>x<sup>4<\/sup>-2x<sup>3<\/sup>+7x<sup>2<\/sup>-2x+1=1\/2(x<sup>2<\/sup>-3x+1)<sup>2<\/sup>+1\/2(x<sup>2<\/sup>+x+1)<sup>2<\/sup><\/em>. Studying the relationship between non-negativity and sums of squares has a distinguished history in mathematics starting with work of David Hilbert and Hilbert&#8217;s 17th problem. I will discuss the history and some modern applications of sums of squares in optimization and combinatorics.<\/p>\n<p>Prof. Blekherman is on the Mathematics faculty at Georgia Tech; he also is an advocate for Georgia Tech&#8217;s internationally renown Algorithms, Combinatorics and Optimization (ACO) graduate program.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Title: Nonnegative Polynomials and Sums of Squares Abstract: Is x4-2&#215;3+7&#215;2-2x+1 nonnegative for any value of x? One way of showing that this holds is by writing x4-2&#215;3+7&#215;2-2x+1=1\/2(x2-3x+1)2+1\/2(x2+x+1)2. Studying the relationship [&hellip;]<\/p>\n","protected":false},"author":82,"featured_media":0,"template":"","meta":{"_acf_changed":false,"_price":"","_stock":"","_tribe_ticket_header":"","_tribe_default_ticket_provider":"","_tribe_ticket_capacity":"0","_ticket_start_date":"","_ticket_end_date":"","_tribe_ticket_show_description":"","_tribe_ticket_show_not_going":false,"_tribe_ticket_use_global_stock":"","_tribe_ticket_global_stock_level":"","_global_stock_mode":"","_global_stock_cap":"","_tribe_rsvp_for_event":"","_tribe_ticket_going_count":"","_tribe_ticket_not_going_count":"","_tribe_tickets_list":"[]","_tribe_ticket_has_attendee_info_fields":false,"_tribe_events_status":"","_tribe_events_status_reason":"","_tribe_events_is_hybrid":"","_tribe_events_is_virtual":"","_tribe_events_virtual_video_source":"","_tribe_events_virtual_embed_video":"","_tribe_events_virtual_linked_button_text":"","_tribe_events_virtual_linked_button":"","_tribe_events_virtual_show_embed_at":"","_tribe_events_virtual_show_embed_to":[],"_tribe_events_virtual_show_on_event":"","_tribe_events_virtual_show_on_views":"","_tribe_events_virtual_url":"","footnotes":"","_tec_slr_enabled":"","_tec_slr_layout":""},"tags":[],"tribe_events_cat":[12],"class_list":["post-2062","tribe_events","type-tribe_events","status-publish","hentry","tribe_events_cat-colloquium","cat_colloquium"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.2 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Prof. Grigoriy Blekherman - Claremont Center for the Mathematical Sciences<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/colleges.claremont.edu\/ccms\/event\/prof-grigoriy-blekherman\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Prof. Grigoriy Blekherman - Claremont Center for the Mathematical Sciences\" \/>\n<meta property=\"og:description\" content=\"Title: Nonnegative Polynomials and Sums of Squares Abstract: Is x4-2x3+7x2-2x+1 nonnegative for any value of x? One way of showing that this holds is by writing x4-2x3+7x2-2x+1=1\/2(x2-3x+1)2+1\/2(x2+x+1)2. Studying the relationship [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/colleges.claremont.edu\/ccms\/event\/prof-grigoriy-blekherman\/\" \/>\n<meta property=\"og:site_name\" content=\"Claremont Center for the Mathematical Sciences\" \/>\n<meta property=\"article:modified_time\" content=\"2020-09-29T14:35:05+00:00\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data1\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/colleges.claremont.edu\/ccms\/event\/prof-grigoriy-blekherman\/\",\"url\":\"https:\/\/colleges.claremont.edu\/ccms\/event\/prof-grigoriy-blekherman\/\",\"name\":\"Prof. Grigoriy Blekherman - Claremont Center for the Mathematical Sciences\",\"isPartOf\":{\"@id\":\"https:\/\/colleges.claremont.edu\/ccms\/#website\"},\"datePublished\":\"2020-09-29T14:34:03+00:00\",\"dateModified\":\"2020-09-29T14:35:05+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/colleges.claremont.edu\/ccms\/event\/prof-grigoriy-blekherman\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/colleges.claremont.edu\/ccms\/event\/prof-grigoriy-blekherman\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/colleges.claremont.edu\/ccms\/event\/prof-grigoriy-blekherman\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/colleges.claremont.edu\/ccms\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Events\",\"item\":\"https:\/\/colleges.claremont.edu\/ccms\/events\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Prof. Grigoriy Blekherman\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/colleges.claremont.edu\/ccms\/#website\",\"url\":\"https:\/\/colleges.claremont.edu\/ccms\/\",\"name\":\"Claremont Center for the Mathematical Sciences\",\"description\":\"Proudly Serving the Math Community at the Claremont Colleges Since 2007\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/colleges.claremont.edu\/ccms\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Prof. Grigoriy Blekherman - Claremont Center for the Mathematical Sciences","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/colleges.claremont.edu\/ccms\/event\/prof-grigoriy-blekherman\/","og_locale":"en_US","og_type":"article","og_title":"Prof. Grigoriy Blekherman - Claremont Center for the Mathematical Sciences","og_description":"Title: Nonnegative Polynomials and Sums of Squares Abstract: Is x4-2x3+7x2-2x+1 nonnegative for any value of x? One way of showing that this holds is by writing x4-2x3+7x2-2x+1=1\/2(x2-3x+1)2+1\/2(x2+x+1)2. 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