\uace0\ub4f1\uacfc\ud559\uc6d0 \ud2b9\uac15\uc785\ub2c8\ub2e4
\nKIAS Quadranscentennial Lectures<\/p>\n
DATE: April 15 (Thu), April 22 (Thu) 2021
\nTIME: 10:00-11:30
\nSPEAKER: Danny Calegari (University of Chicago)
\nTITLE: Sausages and Butcher Paper I, II <\/p>\n
ABSTRACT:
\nThe shift locus S_d is the space of conjugacy classes of degree d polynomials f(z) in one complex variable for which all the critical points tend to infinity under repeated application of f. When d=2 this is the complement of the Mandelbrot set. Although S_d is a very complicated space geometrically, it turns out one can get a surprisingly concrete description of its topology; for example, S_2 is homeomorphic to an open annulus (this is equivalent to the famous theorem of Douady-Hubbard that the Mandelbrot set is connected). I would like to discuss two very explicit ways to capture the topology of S_d, one via the combinatorics of laminations (Butcher paper) and one via algebraic geometry (sausages). As a corollary of this explicit description one can show that S_d is a K(pi,1) with the homotopy type of a complex of half its real dimension.<\/p>\n
\uc90c\uc744 \uc774\uc6a9\ud55c \uc628\ub77c\uc778 \uac15\uc5f0\uc785\ub2c8\ub2e4. \uace0\ub4f1\uacfc\ud559\uc6d0 \uc138\ubbf8\ub098 \uac8c\uc2dc\ud310\uc744 \ucc38\uace0\ud558\uc138\uc694.<\/p>\n","protected":false},"excerpt":{"rendered":"
\uace0\ub4f1\uacfc\ud559\uc6d0 \ud2b9\uac15\uc785\ub2c8\ub2e4 KIAS Quadranscentennial Lectures DATE: April 15 (Thu), April 22 (Thu) 2021 TIME: 10:00-11:30 SPEAKER: Danny Calegari (University of Chicago) TITLE: Sausages and Butcher Paper I, II ABSTRACT: The shift locus S_d is the space of conjugacy classes of degree d polynomials f(z) in one complex variable for which all the critical points tend … \ub354 \uc77d\uae30<\/a><\/p>\n","protected":false},"author":6,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0,"footnotes":""},"categories":[1],"tags":[],"class_list":["post-1054","post","type-post","status-publish","format-standard","hentry","category-news-events"],"distributor_meta":false,"distributor_terms":false,"distributor_media":false,"distributor_original_site_name":"","distributor_original_site_url":"https:\/\/mathematicians.korea.ac.kr\/sk23","push-errors":false,"_links":{"self":[{"href":"https:\/\/mathematicians.korea.ac.kr\/sk23\/wp-json\/wp\/v2\/posts\/1054","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathematicians.korea.ac.kr\/sk23\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathematicians.korea.ac.kr\/sk23\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathematicians.korea.ac.kr\/sk23\/wp-json\/wp\/v2\/users\/6"}],"replies":[{"embeddable":true,"href":"https:\/\/mathematicians.korea.ac.kr\/sk23\/wp-json\/wp\/v2\/comments?post=1054"}],"version-history":[{"count":3,"href":"https:\/\/mathematicians.korea.ac.kr\/sk23\/wp-json\/wp\/v2\/posts\/1054\/revisions"}],"predecessor-version":[{"id":1057,"href":"https:\/\/mathematicians.korea.ac.kr\/sk23\/wp-json\/wp\/v2\/posts\/1054\/revisions\/1057"}],"wp:attachment":[{"href":"https:\/\/mathematicians.korea.ac.kr\/sk23\/wp-json\/wp\/v2\/media?parent=1054"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathematicians.korea.ac.kr\/sk23\/wp-json\/wp\/v2\/categories?post=1054"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathematicians.korea.ac.kr\/sk23\/wp-json\/wp\/v2\/tags?post=1054"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}