{"id":3054,"global_id":"colleges.claremont.edu\/ccms?id=3054","global_id_lineage":["colleges.claremont.edu\/ccms?id=3054"],"author":"73","status":"publish","date":"2023-01-24 13:27:08","date_utc":"2023-01-24 21:27:08","modified":"2023-03-20 15:53:30","modified_utc":"2023-03-20 22:53:30","url":"https:\/\/colleges.claremont.edu\/ccms\/event\/antc-talk-gilyoung-cheong-uci\/","rest_url":"https:\/\/colleges.claremont.edu\/ccms\/wp-json\/tribe\/events\/v1\/events\/3054","title":"The Smith normal form of a polynomial of a random integral matrix (Gilyoung Cheong, UC Irvine)","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 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>\n
This is joint work with Myungjun Yu.\u00a0https:\/\/arxiv.org\/abs\/2303.09125<\/a><\/div>","excerpt":"","slug":"antc-talk-gilyoung-cheong-uci","image":false,"all_day":false,"start_date":"2023-03-28 12:15:00","start_date_details":{"year":"2023","month":"03","day":"28","hour":"12","minutes":"15","seconds":"00"},"end_date":"2023-03-28 13:10:00","end_date_details":{"year":"2023","month":"03","day":"28","hour":"13","minutes":"10","seconds":"00"},"utc_start_date":"2023-03-28 19:15:00","utc_start_date_details":{"year":"2023","month":"03","day":"28","hour":"19","minutes":"15","seconds":"00"},"utc_end_date":"2023-03-28 20:10:00","utc_end_date_details":{"year":"2023","month":"03","day":"28","hour":"20","minutes":"10","seconds":"00"},"timezone":"America\/Los_Angeles","timezone_abbr":"PDT","cost":"","cost_details":{"currency_symbol":"","currency_code":"","currency_position":"","values":[]},"website":"","show_map":true,"show_map_link":true,"hide_from_listings":false,"sticky":false,"featured":false,"categories":[{"name":"Algebra \/ Number Theory \/ Combinatorics Seminar","slug":"antc-seminar","term_group":0,"term_taxonomy_id":13,"taxonomy":"tribe_events_cat","description":"","parent":0,"count":170,"filter":"raw","term_order":"0","id":13,"urls":{"self":"https:\/\/colleges.claremont.edu\/ccms\/wp-json\/tribe\/events\/v1\/categories\/13","collection":"https:\/\/colleges.claremont.edu\/ccms\/wp-json\/tribe\/events\/v1\/categories"}}],"tags":[],"venue":{"id":2841,"author":"73","status":"publish","date":"2022-09-06 16:13:47","date_utc":"2022-09-06 23:13:47","modified":"2022-09-06 16:13:47","modified_utc":"2022-09-06 23:13:47","url":"https:\/\/colleges.claremont.edu\/ccms\/venue\/davidson-lecture-hall-cmc\/","venue":"Davidson Lecture Hall, CMC","slug":"davidson-lecture-hall-cmc","address":"340 E 9th St","city":"Claremont","country":"United States","state":"CA","zip":"91711","website":"https:\/\/www.google.com\/maps\/place\/Davidson+Lecture+Hall\/@34.1023916,-117.7100769,15z\/data=!4m5!3m4!1s0x0:0x16727af9968473b4!8m2!3d34.1023916!4d-117.7100769","stateprovince":"CA","json_ld":{"@type":"Place","name":"Davidson Lecture Hall, CMC","description":"","url":"https:\/\/colleges.claremont.edu\/ccms\/venue\/davidson-lecture-hall-cmc\/","address":{"@type":"PostalAddress","streetAddress":"340 E 9th St","addressLocality":"Claremont","addressRegion":"CA","postalCode":"91711","addressCountry":"United States"},"telephone":"","sameAs":"https:\/\/www.google.com\/maps\/place\/Davidson+Lecture+Hall\/@34.1023916,-117.7100769,15z\/data=!4m5!3m4!1s0x0:0x16727af9968473b4!8m2!3d34.1023916!4d-117.7100769"},"show_map":true,"show_map_link":true,"global_id":"colleges.claremont.edu\/ccms?id=2841","global_id_lineage":["colleges.claremont.edu\/ccms?id=2841"]},"organizer":[{"id":426,"author":"73","status":"publish","date":"2018-08-17 08:08:12","date_utc":"2018-08-17 15:08:12","modified":"2018-08-17 08:08:12","modified_utc":"2018-08-17 15:08:12","url":"https:\/\/colleges.claremont.edu\/ccms\/organizer\/lenny-fukshansky-4\/","organizer":"Lenny Fukshansky","slug":"lenny-fukshansky-4","json_ld":{"@type":"Person","name":"Lenny Fukshansky","description":"","url":"","telephone":"","email":"","sameAs":""},"global_id":"colleges.claremont.edu\/ccms?id=426","global_id_lineage":["colleges.claremont.edu\/ccms?id=426"]},{"id":433,"author":"73","status":"publish","date":"2018-08-08 15:52:55","date_utc":"2018-08-08 22:52:55","modified":"2018-08-08 15:52:55","modified_utc":"2018-08-08 22:52:55","url":"https:\/\/colleges.claremont.edu\/ccms\/organizer\/gizem-karaali-2\/","organizer":"Gizem Karaali","slug":"gizem-karaali-2","json_ld":{"@type":"Person","name":"Gizem Karaali","description":"","url":"","telephone":"","email":"","sameAs":""},"global_id":"colleges.claremont.edu\/ccms?id=433","global_id_lineage":["colleges.claremont.edu\/ccms?id=433"]}],"custom_fields":[],"json_ld":{"@context":"http:\/\/schema.org","@type":"Event","name":"The Smith normal form of a polynomial of a random integral matrix (Gilyoung Cheong, UC Irvine)","description":"<p>Given a prime p, let P(t) be a non-constant monic polynomial in t over the ring of p-adic integers. 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