{"id":5711492,"date":"2022-02-19T17:21:51","date_gmt":"2022-02-20T03:21:51","guid":{"rendered":"https:\/\/math.hawaii.edu\/wordpress\/?p=5711492"},"modified":"2022-02-19T17:22:20","modified_gmt":"2022-02-20T03:22:20","slug":"number-theory-seminars-224","status":"publish","type":"post","link":"https:\/\/math.hawaii.edu\/wordpress\/number-theory-seminars-224\/","title":{"rendered":"Number Theory Seminars 2\/24"},"content":{"rendered":"

\"eisenstein<\/a>Visiting mathematicians from UC San Diego, Alina Bucur and Kiran Kedlaya, will give two number theory talks on Thursday, February 24 in Keller 301.<\/p>\n

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Schedule:<\/b><\/div>\n
3-3:45 PM\u00a0Kiran\u00a0Kedlaya<\/span><\/b><\/div>\n<\/div>\n
The relative class number one problem for function fieldsAbstract:\u00a0Gauss conjectured that there are nine imaginary quadratic fields of class number 1; this was resolved in the 20th century by work\u00a0of Baker, Heegner, and Stark. In between, Artin had introduced the analogy between number fields and function fields, the latter being finite extensions of the field of rational functions over a finite field. In this realm, the class number 1 problem admits multiple analogues; we recall some of these, one of which was “resolved” in 1975 and then falsified (and corrected) in 2014, and another one of which is a brand-new theorem in which computer calculations (in SageMath and Magma) play a pivotal role.<\/p>\n<\/div>\n

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3:45-4:15 PM
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Q&A, break, refreshments<\/div>\n<\/div>\n
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4:15-5 PM\u00a0Alina Bucur
\n<\/b>Counting points on curves over finite fields<\/p>\n

Abstract: A curve is a one dimensional space cut out by polynomial equations. In particular, one can\u00a0consider curves over finite fields, which means the polynomial equations should have coefficients\u00a0in some finite field and that points on the curve are given by values of the variables in the finite field that satisfy the given polynomials. A basic question is how many points such a curve has, and for\u00a0a family of curves one can study the distribution of this statistic. We will give concrete examples\u00a0of families in which this distribution is known or predicted, and give a sense of the different kinds\u00a0of mathematics that are used to study different families. This is joint work with Chantal David, Brooke Feigon, Kiran S.\u00a0Kedlaya<\/span>, and Matilde Lalin.<\/p>\n<\/div>\n<\/div>\n

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Visiting mathematicians from UC San Diego, Alina Bucur and Kiran Kedlaya, will give two number theory talks on Thursday, February 24 in Keller 301. Schedule: 3-3:45 PM\u00a0Kiran\u00a0Kedlaya The relative class number one problem for function fieldsAbstract:\u00a0Gauss conjectured that there are nine imaginary quadratic fields of class number 1; this was resolved in the 20th century … Continue reading Number Theory Seminars 2\/24<\/span> →<\/span><\/a><\/p>\n","protected":false},"author":31,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[60,1],"tags":[],"class_list":["post-5711492","post","type-post","status-publish","format-standard","hentry","category-colloquium","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/math.hawaii.edu\/wordpress\/wp-json\/wp\/v2\/posts\/5711492","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/math.hawaii.edu\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/math.hawaii.edu\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/math.hawaii.edu\/wordpress\/wp-json\/wp\/v2\/users\/31"}],"replies":[{"embeddable":true,"href":"https:\/\/math.hawaii.edu\/wordpress\/wp-json\/wp\/v2\/comments?post=5711492"}],"version-history":[{"count":3,"href":"https:\/\/math.hawaii.edu\/wordpress\/wp-json\/wp\/v2\/posts\/5711492\/revisions"}],"predecessor-version":[{"id":5711496,"href":"https:\/\/math.hawaii.edu\/wordpress\/wp-json\/wp\/v2\/posts\/5711492\/revisions\/5711496"}],"wp:attachment":[{"href":"https:\/\/math.hawaii.edu\/wordpress\/wp-json\/wp\/v2\/media?parent=5711492"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/math.hawaii.edu\/wordpress\/wp-json\/wp\/v2\/categories?post=5711492"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/math.hawaii.edu\/wordpress\/wp-json\/wp\/v2\/tags?post=5711492"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}