{"id":19546,"date":"2025-10-20T12:50:20","date_gmt":"2025-10-20T16:50:20","guid":{"rendered":"https:\/\/www.crmath.ca\/page-calendrier\/speakers-2026-sms-2\/"},"modified":"2025-10-23T16:20:53","modified_gmt":"2025-10-23T20:20:53","slug":"prerequisites-2026-sms","status":"publish","type":"page-calendrier","link":"https:\/\/www.crmath.ca\/en\/page-calendrier\/prerequisites-2026-sms\/","title":{"rendered":"Prerequisites-2026-SMS"},"content":{"rendered":"<div class=\"fusion-fullwidth fullwidth-box fusion-builder-row-1 fusion-flex-container nonhundred-percent-fullwidth non-hundred-percent-height-scrolling\" style=\"--awb-border-radius-top-left:0px;--awb-border-radius-top-right:0px;--awb-border-radius-bottom-right:0px;--awb-border-radius-bottom-left:0px;--awb-flex-wrap:wrap;\" ><div class=\"fusion-builder-row fusion-row fusion-flex-align-items-flex-start fusion-flex-content-wrap\" style=\"max-width:1420.64px;margin-left: calc(-4% \/ 2 );margin-right: calc(-4% \/ 2 );\"><div class=\"fusion-layout-column fusion_builder_column fusion-builder-column-0 fusion_builder_column_1_1 1_1 fusion-flex-column\" style=\"--awb-bg-size:cover;--awb-width-large:100%;--awb-margin-top-large:0px;--awb-spacing-right-large:1.92%;--awb-margin-bottom-large:0px;--awb-spacing-left-large:1.92%;--awb-width-medium:100%;--awb-order-medium:0;--awb-spacing-right-medium:1.92%;--awb-spacing-left-medium:1.92%;--awb-width-small:100%;--awb-order-small:0;--awb-spacing-right-small:1.92%;--awb-spacing-left-small:1.92%;\"><div class=\"fusion-column-wrapper fusion-column-has-shadow fusion-flex-justify-content-flex-start fusion-content-layout-column\"><div class=\"fusion-text fusion-text-1\"><p>Students should be familiar with first courses in algebraic number theory and in analytic number theory.<\/p>\n<p><b>Preparatory Reading for certain mini-courses.\u00a0<\/b>Each of the following are about 30 pages long:<\/p>\n<p>&#8212; Melanie Wood (Harvard):\u00a0&#8220;Probability theory for random groups arising in\u00a0number\u00a0theory&#8221;\u00a0<a href=\"https:\/\/ems.press\/books\/standalone\/278\/5565\" target=\"_blank\" rel=\"noopener\" data-saferedirecturl=\"https:\/\/www.google.com\/url?q=https:\/\/ems.press\/books\/standalone\/278\/5565&amp;source=gmail&amp;ust=1759854270832000&amp;usg=AOvVaw2aRkbTuBOYwuGi1DjKs6bl\">https:\/\/ems.press\/books\/<wbr \/>standalone\/278\/5565<\/a><\/p>\n<p>&#8212; Ashvin Swaminathan (Harvard):\u00a0&#8220;Counting\u00a0Cubic\u00a0Num<wbr \/>ber\u00a0Fields&#8221;\u00a0by Niven Achenjang\u00a0<a href=\"https:\/\/www.mit.edu\/~NivenT\/assets\/pdf\/Counting_Cubic_Number_Fields.pdf\" target=\"_blank\" rel=\"noopener\" data-saferedirecturl=\"https:\/\/www.google.com\/url?q=https:\/\/www.mit.edu\/~NivenT\/assets\/pdf\/Counting_Cubic_Number_Fields.pdf&amp;source=gmail&amp;ust=1759854270832000&amp;usg=AOvVaw14YA35T0DQD6_nDOdogHGO\">https:\/\/www.mit.<wbr \/>edu\/~NivenT\/assets\/pdf\/<wbr \/>Counting_Cubic_Number_Fields.<wbr \/>pdf<\/a>.<\/p>\n<p>&#8212; Adam Harper &#8220;Moments of random multiplicative functions, III: A short review&#8221;\u00a0<a href=\"https:\/\/arxiv.org\/abs\/2410.11523\" target=\"_blank\" rel=\"noopener\" data-saferedirecturl=\"https:\/\/www.google.com\/url?q=https:\/\/arxiv.org\/abs\/2410.11523&amp;source=gmail&amp;ust=1759854270832000&amp;usg=AOvVaw06yPm5qcDWkZgoHrTJaBBA\">https:\/\/arxiv.org\/abs\/<wbr \/>2410.11523<\/a>, &amp; the introduction of &#8220;On the limiting distribution of sums of random multiplicative functions&#8221; \u00a0<a href=\"https:\/\/arxiv.org\/abs\/2508.12956\" target=\"_blank\" rel=\"noopener\" data-saferedirecturl=\"https:\/\/www.google.com\/url?q=https:\/\/arxiv.org\/abs\/2508.12956&amp;source=gmail&amp;ust=1759854270832000&amp;usg=AOvVaw20C74-uq7gnRbChL_V2qeI\">https:\/\/arxiv.org\/abs\/2508.<wbr \/>12956<\/a><\/p>\n<p>&#8212; Alexandra Florea (UC Irvine): &#8220;Traces of high powers of the Frobenius class in the hyperelliptic ensemble&#8221; by Zeev Rudnick, Acta Arithmetic, 143.1 (2010), 81-99, obtain from this <a href=\"https:\/\/www.impan.pl\/en\/publishing-house\/journals-and-series\/acta-arithmetica\/en\/publishing-house\/journals-and-series\/acta-arithmetica\/all\/143\">LINK<\/a><\/p>\n<p>&#8212; Alex Smith: &#8220;The Selmer group, the Shafarevich-Tate group, and the weak Mordell Weil theorem&#8221; by Bjorn Poonen\u00a0<a href=\"https:\/\/math.mit.edu\/~poonen\/f01\/weakmw.pdf\" target=\"_blank\" rel=\"noopener\" data-saferedirecturl=\"https:\/\/www.google.com\/url?q=https:\/\/math.mit.edu\/~poonen\/f01\/weakmw.pdf&amp;source=gmail&amp;ust=1759854270832000&amp;usg=AOvVaw19in61ArS6Cr449U1zYnNk\">https:\/\/math.mit.edu\/~poonen\/<wbr \/>f01\/weakmw.pdf<\/a><\/p>\n<p>&#8212; Tim Browning (IST Austria):\u00a0&#8220;Beginners guide \u00a0to the circle method&#8221; by Andrew Granville\u00a0<a href=\"https:\/\/dms.umontreal.ca\/~andrew\/CircleMethodNotes.pdf\">https:\/\/dms.umontreal.ca\/~andrew\/CircleMethodNotes.pdf<\/a><\/p>\n<\/div><\/div><\/div><\/div><\/div>\n","protected":false},"author":18,"template":"","class_list":["post-19546","page-calendrier","type-page-calendrier","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.crmath.ca\/en\/wp-json\/wp\/v2\/page-calendrier\/19546","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.crmath.ca\/en\/wp-json\/wp\/v2\/page-calendrier"}],"about":[{"href":"https:\/\/www.crmath.ca\/en\/wp-json\/wp\/v2\/types\/page-calendrier"}],"author":[{"embeddable":true,"href":"https:\/\/www.crmath.ca\/en\/wp-json\/wp\/v2\/users\/18"}],"version-history":[{"count":4,"href":"https:\/\/www.crmath.ca\/en\/wp-json\/wp\/v2\/page-calendrier\/19546\/revisions"}],"predecessor-version":[{"id":19624,"href":"https:\/\/www.crmath.ca\/en\/wp-json\/wp\/v2\/page-calendrier\/19546\/revisions\/19624"}],"wp:attachment":[{"href":"https:\/\/www.crmath.ca\/en\/wp-json\/wp\/v2\/media?parent=19546"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}