{"id":24,"date":"2026-04-09T09:13:32","date_gmt":"2026-04-09T09:13:32","guid":{"rendered":"https:\/\/musbahu-idris.apps.math.cnrs.fr\/?page_id=24"},"modified":"2026-05-26T13:28:59","modified_gmt":"2026-05-26T13:28:59","slug":"communications","status":"publish","type":"page","link":"https:\/\/musbahu-idris.apps.math.cnrs.fr\/?page_id=24","title":{"rendered":"Communications"},"content":{"rendered":"<ul>\n<li><strong>Algorithmic Aspects of Newman Polynomials and Their Divisors<\/strong><br \/>\nS\u00e9minaire des doctorants, 13 mai 2026<br \/>\n<em>\u00a0 \u00a0 \u00a0A Newman polynomial is a polynomial with coefficients in {0,1} and constant term 1. We investigate which integer-coefficient polynomials divide a Newman polynomial, focusing on those with small Mahler measure. Using mixed-integer linear programming, we determine the divisibility status of all 8,438 known polynomials with Mahler measure less than 1.3. We further exhibit new polynomials that divide no Newman polynomial, improving the best known upper bound on a conjectural universal constant \u03c3 to approximately 1.419.<\/em><\/li>\n<li style=\"text-align: justify;\"><strong>Algorithmic Aspects of Newman Polynomials and Their Divisors<br \/>\n<\/strong>Luxembourg PHD Seminar Days, 22 mai 2026<br \/>\n<em>\u00a0 \u00a0 A Newman polynomial is a polynomial whose coefficients belong to <span class=\"katex\"><span class=\"katex-mathml\">{0,1}<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mopen\">{<\/span><span class=\"mord\">0<\/span><span class=\"mpunct\">,<\/span><span class=\"mord\">1<\/span><span class=\"mclose\">}<\/span><\/span><\/span><\/span> and whose constant term is equal to <span class=\"katex\"><span class=\"katex-mathml\">1<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">1<\/span><\/span><\/span><\/span>. In this talk, we study the problem of deciding which integer polynomials can occur as divisors of Newman polynomials, with particular attention to polynomials of small Mahler measure. By formulating the divisibility problem as a mixed-integer linear programming problem, we determine the status of all <span class=\"katex\"><span class=\"katex-mathml\">8,438<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">8<\/span><span class=\"mord\"><span class=\"mpunct\">,<\/span><\/span><span class=\"mord\">438<\/span><\/span><\/span><\/span> known polynomials with Mahler measure below <span class=\"katex\"><span class=\"katex-mathml\">1.3<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">1.3<\/span><\/span><\/span><\/span>. We also construct new examples of polynomials that do not divide any Newman polynomial, thereby lowering the best known upper bound for the conjectural universal constant <span class=\"katex\"><span class=\"katex-mathml\">\u03c3<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">\u03c3<\/span><\/span><\/span><\/span> to approximately <span class=\"katex\"><span class=\"katex-mathml\">1.419<\/span><\/span>.<\/em><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Algorithmic Aspects of Newman Polynomials and Their Divisors S\u00e9minaire des doctorants, 13 mai 2026 \u00a0 \u00a0 \u00a0A Newman polynomial is a polynomial with coefficients in {0,1} and constant term 1. We investigate which integer-coefficient polynomials divide a Newman polynomial, focusing on those with small Mahler measure. Using mixed-integer linear programming, we determine the divisibility status &hellip; <a href=\"https:\/\/musbahu-idris.apps.math.cnrs.fr\/?page_id=24\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Communications<\/span> <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-24","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/musbahu-idris.apps.math.cnrs.fr\/index.php?rest_route=\/wp\/v2\/pages\/24","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/musbahu-idris.apps.math.cnrs.fr\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/musbahu-idris.apps.math.cnrs.fr\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/musbahu-idris.apps.math.cnrs.fr\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/musbahu-idris.apps.math.cnrs.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=24"}],"version-history":[{"count":11,"href":"https:\/\/musbahu-idris.apps.math.cnrs.fr\/index.php?rest_route=\/wp\/v2\/pages\/24\/revisions"}],"predecessor-version":[{"id":80,"href":"https:\/\/musbahu-idris.apps.math.cnrs.fr\/index.php?rest_route=\/wp\/v2\/pages\/24\/revisions\/80"}],"wp:attachment":[{"href":"https:\/\/musbahu-idris.apps.math.cnrs.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=24"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}