{"id":3059,"date":"2025-11-19T11:51:42","date_gmt":"2025-11-19T09:51:42","guid":{"rendered":"https:\/\/mathematics.haifa.ac.il\/?p=3059"},"modified":"2025-11-26T12:09:22","modified_gmt":"2025-11-26T10:09:22","slug":"colloquium-tuesday-nov-25-2025-1400-room-614-speaker-boris-shapiro-stockholm-title-return-of-the-plane-evolute","status":"publish","type":"post","link":"https:\/\/mathematics.haifa.ac.il\/?p=3059","title":{"rendered":"Colloquium: Tuesday Nov. 25, 2025 (14:00, room 614). Speaker: Boris Shapiro (Stockholm). Title: &#8220;Return of the plane evolute&#8221;."},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">We consider the evolutes of plane real-algebraic curves and find lower bounds for the following 4\u00a0quantities:\u00a0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">(1) the maximal number of times a real line can intersect the evolute of a real-algebraic curve of degree d;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">(2) the maximal number of real cusps which can occur on the evolute of a real-algebraic curve of degree d;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">(3) the maximal number of crunodes which can occur on the dual curve to the evolute of a real-algebraic curve of degree d;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">(4) the maximal number of crunodes which can occur on the evolute of a real-algebraic curve of degree d.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>We consider the evolutes of plane real-algebraic curves and find lower bounds for the following 4\u00a0quantities:\u00a0 (1) the maximal number of times a real line can intersect the evolute of a real-algebraic curve of degree d; (2) the maximal number&#8230;<br \/><a class=\"read-more-button\" href=\"https:\/\/mathematics.haifa.ac.il\/?p=3059\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[],"class_list":["post-3059","post","type-post","status-publish","format-standard","hentry","category-colloquium"],"_links":{"self":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/3059","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=3059"}],"version-history":[{"count":1,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/3059\/revisions"}],"predecessor-version":[{"id":3060,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/3059\/revisions\/3060"}],"wp:attachment":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3059"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3059"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3059"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}