{"id":251,"date":"2025-11-19T17:56:48","date_gmt":"2025-11-19T16:56:48","guid":{"rendered":"https:\/\/perso.imj-prg.fr\/antonin-guilloux\/?page_id=251"},"modified":"2025-12-08T17:22:12","modified_gmt":"2025-12-08T16:22:12","slug":"famed-exploration-of-andersen-kashaev-volume-conjecture","status":"publish","type":"page","link":"https:\/\/perso.imj-prg.fr\/antonin-guilloux\/famed-exploration-of-andersen-kashaev-volume-conjecture\/","title":{"rendered":"The FAMED project"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">Exploration of Andersen-Kashaev volume conjecture<\/h2>\n\n\n\n<p>Ben Aribi and Wong have described a <a href=\"https:\/\/arxiv.org\/abs\/2410.10776\">combinatorial \u00ab\u00a0FAMED\u00a0\u00bb condition<\/a> on an ideal triangulation of a knot complement under which Andersen-Kashaev volume conjecture holds.<\/p>\n\n\n\n<p>I wrote a SageMath module \u00ab\u00a0FAMEDexploration\u00a0\u00bb, that relies on Regina and Snappy, to try and explore how often this condition hold. It is available <a href=\"https:\/\/plmlab.math.cnrs.fr\/guilloux\/FAMEDexploration\">in this GitLab repository<\/a>. The answer seems very clear: always for a hyperbolic knot complement!<\/p>\n\n\n\n<p>Beware, there is a subtlety! We explored snappy&rsquo;s census HTLinks for 42 136 knot complements with at most 14 crossings and at most 23 tetrahedra. For all but 6 cases, we find a triangulation (often not the one readily given by Snappy) that has the FAMED property, thus proving Andersen-Kashaev conjecture for as many examples.<\/p>\n\n\n\n<p>A regina container containing all those triangulations is available <a href=\"https:\/\/perso.imj-prg.fr\/antonin-guilloux\/wp-content\/uploads\/guilloux-pub\/Organized_at_most_23_tets.rga\">here<\/a>.<\/p>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Exploration of Andersen-Kashaev volume conjecture Ben Aribi and Wong have described a combinatorial \u00ab\u00a0FAMED\u00a0\u00bb condition on an ideal triangulation of a knot complement under which Andersen-Kashaev volume conjecture holds. I wrote a SageMath module \u00ab\u00a0FAMEDexploration\u00a0\u00bb, that relies on Regina and Snappy, to try and explore how often this condition hold. It is available in this [&hellip;]<\/p>\n","protected":false},"author":50,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-251","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/perso.imj-prg.fr\/antonin-guilloux\/wp-json\/wp\/v2\/pages\/251","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/perso.imj-prg.fr\/antonin-guilloux\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/perso.imj-prg.fr\/antonin-guilloux\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/perso.imj-prg.fr\/antonin-guilloux\/wp-json\/wp\/v2\/users\/50"}],"replies":[{"embeddable":true,"href":"https:\/\/perso.imj-prg.fr\/antonin-guilloux\/wp-json\/wp\/v2\/comments?post=251"}],"version-history":[{"count":5,"href":"https:\/\/perso.imj-prg.fr\/antonin-guilloux\/wp-json\/wp\/v2\/pages\/251\/revisions"}],"predecessor-version":[{"id":271,"href":"https:\/\/perso.imj-prg.fr\/antonin-guilloux\/wp-json\/wp\/v2\/pages\/251\/revisions\/271"}],"wp:attachment":[{"href":"https:\/\/perso.imj-prg.fr\/antonin-guilloux\/wp-json\/wp\/v2\/media?parent=251"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}