{"id":3972,"date":"2026-01-22T21:35:57","date_gmt":"2026-01-23T05:35:57","guid":{"rendered":"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&#038;p=3972"},"modified":"2026-04-14T22:34:35","modified_gmt":"2026-04-15T05:34:35","slug":"antc-talk-sehun-jeong-cmc","status":"publish","type":"tribe_events","link":"https:\/\/colleges.claremont.edu\/ccms\/event\/antc-talk-sehun-jeong-cmc\/","title":{"rendered":"Diophantine avoidance, primitive elements, and normal basis theorem (Sehun Jeong, CMC)"},"content":{"rendered":"<p>Diophantine avoidance has been studied by several authors in recent years. This refers to effective results on existence of points of bounded size in a given algebraic set avoiding some specified subsets. The famous primitive element theorem states that every number field\u00a0<i>K<\/i>\u00a0is of the form Q(a) for some element a in\u00a0<i>K<\/i>. From the proof of this theorem, it is clear that not only there are infinitely many such primitive elements in\u00a0<i>K<\/i>, but in fact most elements in\u00a0<i>K<\/i>\u00a0are primitive. One natural question to ask is about finding a primitive element of small &#8220;size&#8221;, where we use a height function to measure size. We discuss the conjecture of Ruppert and known results in this direction, as well as our recent work on this problem. In addition, we provide the standard and effective version of normal basis theorem, obtaining an explicit bound in terms of the degree and discriminant of\u00a0<i>K,\u00a0<\/i>where\u00a0<i>K\/<\/i>Q is a Galois extension. At the end, we discuss a particularly good bound in the case of prime degree. <span data-olk-copy-source=\"MessageBody\">This is joint work with Lenny Fukshansky.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Diophantine avoidance has been studied by several authors in recent years. This refers to effective results on existence of points of bounded size in a given algebraic set avoiding some [&hellip;]<\/p>\n","protected":false},"author":73,"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":[13],"class_list":["post-3972","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 v28.3 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Diophantine avoidance, primitive elements, and normal basis theorem (Sehun Jeong, CMC) - 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\/antc-talk-sehun-jeong-cmc\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Diophantine avoidance, primitive elements, and normal basis theorem (Sehun Jeong, CMC) - Claremont Center for the Mathematical Sciences\" \/>\n<meta property=\"og:description\" content=\"Diophantine avoidance has been studied by several authors in recent years. This refers to effective results on existence of points of bounded size in a given algebraic set avoiding some [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/colleges.claremont.edu\/ccms\/event\/antc-talk-sehun-jeong-cmc\/\" \/>\n<meta property=\"og:site_name\" content=\"Claremont Center for the Mathematical Sciences\" \/>\n<meta property=\"article:modified_time\" content=\"2026-04-15T05:34:35+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\\\/antc-talk-sehun-jeong-cmc\\\/\",\"url\":\"https:\\\/\\\/colleges.claremont.edu\\\/ccms\\\/event\\\/antc-talk-sehun-jeong-cmc\\\/\",\"name\":\"Diophantine avoidance, primitive elements, and normal basis theorem (Sehun Jeong, CMC) - Claremont Center for the Mathematical Sciences\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/colleges.claremont.edu\\\/ccms\\\/#website\"},\"datePublished\":\"2026-01-23T05:35:57+00:00\",\"dateModified\":\"2026-04-15T05:34:35+00:00\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/colleges.claremont.edu\\\/ccms\\\/event\\\/antc-talk-sehun-jeong-cmc\\\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/colleges.claremont.edu\\\/ccms\\\/event\\\/antc-talk-sehun-jeong-cmc\\\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/colleges.claremont.edu\\\/ccms\\\/event\\\/antc-talk-sehun-jeong-cmc\\\/#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\":\"Diophantine avoidance, primitive elements, and normal basis theorem (Sehun Jeong, 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":"Diophantine avoidance, primitive elements, and normal basis theorem (Sehun Jeong, CMC) - 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\/antc-talk-sehun-jeong-cmc\/","og_locale":"en_US","og_type":"article","og_title":"Diophantine avoidance, primitive elements, and normal basis theorem (Sehun Jeong, CMC) - Claremont Center for the Mathematical Sciences","og_description":"Diophantine avoidance has been studied by several authors in recent years. 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