{"id":1468,"date":"2025-09-30T15:47:45","date_gmt":"2025-09-30T15:47:45","guid":{"rendered":"https:\/\/as.vanderbilt.edu\/math\/?p=1468"},"modified":"2026-02-19T17:38:40","modified_gmt":"2026-02-19T17:38:40","slug":"colloquium-talk-by-alexander-dunn-october-7-2025","status":"publish","type":"post","link":"https:\/\/as.vanderbilt.edu\/math\/2025\/09\/30\/colloquium-talk-by-alexander-dunn-october-7-2025\/","title":{"rendered":"Colloquium \u2013 Talk by Alexander Dunn: October 7, 2025"},"content":{"rendered":"<p>October 7, 2025 (Wednesday), 4:10 pm<\/p>\n<p>Alexander Dunn, Georgia Institute of Technology<\/p>\n<p><strong><span class=\"a_GcMg font-feature-liga-off font-feature-clig-off font-feature-calt-off text-decoration-none text-strikethrough-none\"><span data-teams=\"true\">Recent progress on Gauss sums and primes<\/span><\/span><\/strong><\/p>\n<p>Large sieve inequalities are a fundamental tool used to investigate prime numbers and exponential sums.\u00a0In this Colloquium I will explain my work that resolves a\u00a01978 conjecture of S.\u00a0Patterson (conditional on the Generalized Riemann hypothesis)\u00a0concerning the bias of cubic Gauss sums over the prime numbers.\u00a0This explains a well-known numerical bias\u00a0first observed by Kummer in 1846. This bias was later the subject of testing on some of the first super computers in the 20th century.\u00a0Recent and related progress on higher order Gauss sums will also be outlined.\u00a0This work sheds light on some of the mysteries surrounding large sieve inequalities and gives us clues on where to look next for more progress.<\/p>\n<p>This is based on serval joint works with\u00a0various collaborators: Maksym Radziwill, Chantal David, Alia Hamieh, and Hua Lin<\/p>\n","protected":false},"excerpt":{"rendered":"<p>October 7, 2025 (Wednesday), 4:10 pm Alexander Dunn, Georgia Institute of Technology Recent progress on Gauss sums and primes Large sieve inequalities are a fundamental tool used to investigate prime numbers and exponential sums.\u00a0In this Colloquium I will explain my work that resolves a\u00a01978 conjecture of S.\u00a0Patterson (conditional on the Generalized Riemann hypothesis)\u00a0concerning the bias&#8230;<\/p>\n","protected":false},"author":208,"featured_media":1663,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[7,6],"tags":[],"acf":[],"jetpack_featured_media_url":"https:\/\/as.vanderbilt.edu\/math\/wp-content\/uploads\/sites\/69\/2025\/09\/Untitled-design-10-scaled.jpg","_links":{"self":[{"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/posts\/1468"}],"collection":[{"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/users\/208"}],"replies":[{"embeddable":true,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/comments?post=1468"}],"version-history":[{"count":3,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/posts\/1468\/revisions"}],"predecessor-version":[{"id":1482,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/posts\/1468\/revisions\/1482"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/media\/1663"}],"wp:attachment":[{"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/media?parent=1468"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/categories?post=1468"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/tags?post=1468"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}