{"date":"2022-04-04","starts":{"hour":11,"minute":0,"second":0,"second_of_day":39600},"ends":{"hour":12,"minute":0,"second":0,"second_of_day":43200},"room":"32/114","speaker":"Chris Phillips","from":"University of Oregon","title":"The Radius of Comparison of a Commutative C*-algebra","abstract":"The radius of comparison of a C*-algebra is one measure of\r\nthe generalization to C*-algebras of the dimension of a compact\r\nspace. Part of the Toms-Winter conjecture says, informally, that a\r\nsimple separable nuclear unital C*-algebra satisfying the UCT is\r\nclassifiable if and only if its radius of comparison is zero.\r\nNonzero radius of comparison played a key role in one of the main\r\nfamilies of counterexamples to the original form of the Elliott\r\nclassification program.\r\n\r\nIt has been known for some time that the radius of comparison of\r\nC (X) is, ignoring additive constants, at most half the covering\r\ndimension of X. (The factor 1/2 appears because of the use of\r\ncomplex scalars in C*-algebras.) In 2013, Elliott and Niu used Chern\r\ncharacter arguments to show that the radius of comparison of C (X)\r\nis, again ignoring additive constants, at least half the rational\r\ncohomological dimension of X. This left open the question of which\r\ndimension the radius of comparison is really related to. The\r\nrational cohomological dimension can be strictly less than the\r\ninteger cohomological dimension, and there are spaces with integer\r\ncohomological dimension 3 but infinite covering dimension.\r\n\r\nWe show that, up to a slightly worse additive constant, the radius\r\nof comparison of C (X) is at least half the covering dimension of X.\r\nThe proof is fairly short and uses little machinery.","speaker_web":null,"announcement":null,"descfiles_signed_ids":"[]","online":false,"slug":"2022-04-04","shift":{"beginning":{"hour":11,"minute":0,"second":0,"second_of_day":39600},"ending":{"hour":12,"minute":0,"second":0,"second_of_day":43200},"exclude_end":false,"range":"[39600,43200]"},"announcement_i18n":{"en":"","he":""},"duration":"[2022-04-04 08:00:00 UTC,2022-04-04 09:00:00 UTC]","id":885,"created_at":"2022-03-31T00:04:36.387+03:00","updated_at":"2022-03-31T00:04:36.387+03:00","admin_users":[],"summary":"Chris Phillips: The Radius of Comparison of a Commutative C*-algebra","full_speaker_text":"Chris Phillips (*University of Oregon*)","unusual":null,"unusual_place":false,"unusual_time":false,"unusual_day":false}