{"id":3054,"date":"2023-01-24T13:27:08","date_gmt":"2023-01-24T21:27:08","guid":{"rendered":"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&#038;p=3054"},"modified":"2023-03-20T15:53:30","modified_gmt":"2023-03-20T22:53:30","slug":"antc-talk-gilyoung-cheong-uci","status":"publish","type":"tribe_events","link":"https:\/\/colleges.claremont.edu\/ccms\/event\/antc-talk-gilyoung-cheong-uci\/","title":{"rendered":"The Smith normal form of a polynomial of a random integral matrix (Gilyoung Cheong, UC Irvine)"},"content":{"rendered":"<div>Given a prime p, let P(t) be a non-constant monic polynomial in t over the ring of p-adic integers. Let X(n) be an n x n uniformly random (0,1)-matrix over the same ring. We compute the asymptotic distribution of the cokernel of P(X(n)) as n goes to infinity. When P(t) is square-free modulo p, this lets us compute the asymptotic distribution of the Smith normal form of P(X(n)). In fact, we shall consider the same problem with a more general random matrix X(n), which also includes the example of a Haar-random matrix. Our work crucially uses a recent work of W. Sawin and M. M. Wood which shows that the moments of finite size modules over any ring determine their distribution.<\/div>\n<div><\/div>\n<div>This is joint work with Myungjun Yu.\u00a0<a title=\"Original URL: https:\/\/arxiv.org\/abs\/2303.09125. Click or tap if you trust this link.\" href=\"https:\/\/nam12.safelinks.protection.outlook.com\/?url=https%3A%2F%2Farxiv.org%2Fabs%2F2303.09125&amp;data=05%7C01%7Clenny%40cmc.edu%7Ce85efd19ad344860cde608db2990343e%7C60ad6c608a6c4375b276746bfe08cbdf%7C0%7C0%7C638149471554277353%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&amp;sdata=0EFQ5rVh5sCsKhs5auh3oG0Pfx9z%2BZ5J%2FWPf2cmV9SY%3D&amp;reserved=0\" target=\"_blank\" rel=\"noopener noreferrer\" data-auth=\"Verified\" data-linkindex=\"1\">https:\/\/arxiv.org\/abs\/2303.09125<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Given a prime p, let P(t) be a non-constant monic polynomial in t over the ring of p-adic integers. Let X(n) be an n x n uniformly random (0,1)-matrix over [&hellip;]<\/p>\n","protected":false},"author":73,"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":[13],"class_list":["post-3054","tribe_events","type-tribe_events","status-publish","hentry","tribe_events_cat-antc-seminar","cat_antc-seminar"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.2 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>The Smith normal form of a polynomial of a random integral matrix (Gilyoung Cheong, UC Irvine) - 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\/?post_type=tribe_events&p=3054\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The Smith normal form of a polynomial of a random integral matrix (Gilyoung Cheong, UC Irvine) - Claremont Center for the Mathematical Sciences\" \/>\n<meta property=\"og:description\" content=\"Given a prime p, let P(t) be a non-constant monic polynomial in t over the ring of p-adic integers. Let X(n) be an n x n uniformly random (0,1)-matrix over [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&amp;p=3054\" \/>\n<meta property=\"og:site_name\" content=\"Claremont Center for the Mathematical Sciences\" \/>\n<meta property=\"article:modified_time\" content=\"2023-03-20T22:53:30+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\/?post_type=tribe_events&p=3054\",\"url\":\"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&p=3054\",\"name\":\"The Smith normal form of a polynomial of a random integral matrix (Gilyoung Cheong, UC Irvine) - Claremont Center for the Mathematical Sciences\",\"isPartOf\":{\"@id\":\"https:\/\/colleges.claremont.edu\/ccms\/#website\"},\"datePublished\":\"2023-01-24T21:27:08+00:00\",\"dateModified\":\"2023-03-20T22:53:30+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&p=3054#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&p=3054\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&p=3054#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\":\"ANTC talk &#8212; Helen Wong (CMC)\"}]},{\"@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":"The Smith normal form of a polynomial of a random integral matrix (Gilyoung Cheong, UC Irvine) - 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\/?post_type=tribe_events&p=3054","og_locale":"en_US","og_type":"article","og_title":"The Smith normal form of a polynomial of a random integral matrix (Gilyoung Cheong, UC Irvine) - Claremont Center for the Mathematical Sciences","og_description":"Given a prime p, let P(t) be a non-constant monic polynomial in t over the ring of p-adic integers. Let X(n) be an n x n uniformly random (0,1)-matrix over [&hellip;]","og_url":"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&p=3054","og_site_name":"Claremont Center for the Mathematical Sciences","article_modified_time":"2023-03-20T22:53:30+00:00","twitter_card":"summary_large_image","twitter_misc":{"Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&p=3054","url":"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&p=3054","name":"The Smith normal form of a polynomial of a random integral matrix (Gilyoung Cheong, UC Irvine) - Claremont Center for the Mathematical Sciences","isPartOf":{"@id":"https:\/\/colleges.claremont.edu\/ccms\/#website"},"datePublished":"2023-01-24T21:27:08+00:00","dateModified":"2023-03-20T22:53:30+00:00","breadcrumb":{"@id":"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&p=3054#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&p=3054"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&p=3054#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":"ANTC talk &#8212; Helen Wong (CMC)"}]},{"@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"}]}},"ticketed":false,"_links":{"self":[{"href":"https:\/\/colleges.claremont.edu\/ccms\/wp-json\/wp\/v2\/tribe_events\/3054","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/colleges.claremont.edu\/ccms\/wp-json\/wp\/v2\/tribe_events"}],"about":[{"href":"https:\/\/colleges.claremont.edu\/ccms\/wp-json\/wp\/v2\/types\/tribe_events"}],"author":[{"embeddable":true,"href":"https:\/\/colleges.claremont.edu\/ccms\/wp-json\/wp\/v2\/users\/73"}],"version-history":[{"count":0,"href":"https:\/\/colleges.claremont.edu\/ccms\/wp-json\/wp\/v2\/tribe_events\/3054\/revisions"}],"wp:attachment":[{"href":"https:\/\/colleges.claremont.edu\/ccms\/wp-json\/wp\/v2\/media?parent=3054"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/colleges.claremont.edu\/ccms\/wp-json\/wp\/v2\/tags?post=3054"},{"taxonomy":"tribe_events_cat","embeddable":true,"href":"https:\/\/colleges.claremont.edu\/ccms\/wp-json\/wp\/v2\/tribe_events_cat?post=3054"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}