{"id":4334,"date":"2026-09-13T14:33:53","date_gmt":"2026-09-13T21:33:53","guid":{"rendered":"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&#038;p=4334"},"modified":"2026-09-13T14:33:53","modified_gmt":"2026-09-13T21:33:53","slug":"edge-ideals-via-independence-polynomials-of-graphs-dalena-vien-bryn-mawr","status":"publish","type":"tribe_events","link":"https:\/\/colleges.claremont.edu\/ccms\/event\/edge-ideals-via-independence-polynomials-of-graphs-dalena-vien-bryn-mawr\/","title":{"rendered":"Edge Ideals via Independence Polynomials of Graphs \u2014 Dalena Vien (Bryn Mawr)"},"content":{"rendered":"<p>Abstract:\u00a0Edge ideals of graphs provide a fertile ground for uncovering combinatorial expressions for algebraic invariants of squarefree monomial ideals. Many algebraic invariants of these edge ideals directly reflect combinatorial properties of their underlying graphs. In this talk, I will discuss how the independence polynomial \\(P_G(x)\\), the generating function for independent sets of a graph \\(G\\), encodes surprisingly rich information about the Hilbert series of the corresponding edge ideal \\(I(G)\\). In particular, I will explain how \\(P_G(x)\\) determines both the top coefficient and degree of the \\(h\\)-polynomial. I will then demonstrate the results through familiar examples and a simple suspension construction that lets us track these invariants cleanly.<\/p>\n<div style=\"height: 50px;\"><\/div>\n<p style=\"border-bottom: 3px solid #000;\">\n<div style=\"height: 50px;\"><\/div>\n<p>For questions about the event, please contact your CCMS Colloquium chairs:<\/p>\n<p>Prof. Robert Cass (<a href=\"mailto:Robert.Cass@ClaremontMcKenna.edu\">Robert.Cass@ClaremontMcKenna.edu<\/a>) or Prof. Qidi Peng (<a href=\"mailto:Qidi.Peng@cgu.edu\">Qidi.Peng@cgu.edu<\/a>)<\/p>\n<p>For logistical questions, contact Maxwell Kooiker (<a href=\"mailto:Maxwell.Kooiker@cgu.edu\">Maxwell.Kooiker@cgu.edu<\/a>), the CCMS Colloquium Assistant.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Abstract:\u00a0Edge ideals of graphs provide a fertile ground for uncovering combinatorial expressions for algebraic invariants of squarefree monomial ideals. Many algebraic invariants of these edge ideals directly reflect combinatorial properties [&hellip;]<\/p>\n","protected":false},"author":278,"featured_media":0,"template":"","meta":{"_acf_changed":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":""},"tags":[],"tribe_events_cat":[12],"class_list":["post-4334","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 v28.3 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Edge Ideals via Independence Polynomials of Graphs \u2014 Dalena Vien (Bryn Mawr) - 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\/edge-ideals-via-independence-polynomials-of-graphs-dalena-vien-bryn-mawr\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Edge Ideals via Independence Polynomials of Graphs \u2014 Dalena Vien (Bryn Mawr) - Claremont Center for the Mathematical Sciences\" \/>\n<meta property=\"og:description\" content=\"Abstract:\u00a0Edge ideals of graphs provide a fertile ground for uncovering combinatorial expressions for algebraic invariants of squarefree monomial ideals. Many algebraic invariants of these edge ideals directly reflect combinatorial properties [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/colleges.claremont.edu\/ccms\/event\/edge-ideals-via-independence-polynomials-of-graphs-dalena-vien-bryn-mawr\/\" \/>\n<meta property=\"og:site_name\" content=\"Claremont Center for the Mathematical Sciences\" \/>\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\\\/edge-ideals-via-independence-polynomials-of-graphs-dalena-vien-bryn-mawr\\\/\",\"url\":\"https:\\\/\\\/colleges.claremont.edu\\\/ccms\\\/event\\\/edge-ideals-via-independence-polynomials-of-graphs-dalena-vien-bryn-mawr\\\/\",\"name\":\"Edge Ideals via Independence Polynomials of Graphs \u2014 Dalena Vien (Bryn Mawr) - Claremont Center for the Mathematical Sciences\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/colleges.claremont.edu\\\/ccms\\\/#website\"},\"datePublished\":\"2026-09-13T21:33:53+00:00\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/colleges.claremont.edu\\\/ccms\\\/event\\\/edge-ideals-via-independence-polynomials-of-graphs-dalena-vien-bryn-mawr\\\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/colleges.claremont.edu\\\/ccms\\\/event\\\/edge-ideals-via-independence-polynomials-of-graphs-dalena-vien-bryn-mawr\\\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/colleges.claremont.edu\\\/ccms\\\/event\\\/edge-ideals-via-independence-polynomials-of-graphs-dalena-vien-bryn-mawr\\\/#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\":\"Edge Ideals via Independence Polynomials of Graphs \u2014 Dalena Vien (Bryn Mawr)\"}]},{\"@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":"Edge Ideals via Independence Polynomials of Graphs \u2014 Dalena Vien (Bryn Mawr) - 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\/edge-ideals-via-independence-polynomials-of-graphs-dalena-vien-bryn-mawr\/","og_locale":"en_US","og_type":"article","og_title":"Edge Ideals via Independence Polynomials of Graphs \u2014 Dalena Vien (Bryn Mawr) - Claremont Center for the Mathematical Sciences","og_description":"Abstract:\u00a0Edge ideals of graphs provide a fertile ground for uncovering combinatorial expressions for algebraic invariants of squarefree monomial ideals. 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