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X-WR-CALDESC:Събития за Institute of Mathematics and Informatics
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DTSTART;TZID=Europe/Sofia:20231114T140000
DTEND;TZID=Europe/Sofia:20231114T153000
DTSTAMP:20260507T082651
CREATED:20231010T083449Z
LAST-MODIFIED:20231010T090357Z
UID:15136-1699970400-1699975800@math.bas.bg
SUMMARY:Семинар на МЦМН
DESCRIPTION:Дата: 14.11.2023 г.\, 14:00 ч. \nМясто: Зала 403\, ИМИ – БАН \nДокладчик: Валдемар Цанов\, ИМИ – БАН \nКурс: Invariant theory\, homogeneous projective varieties\, and momentum maps \nРезюме: Let \(f:K\to U(V)\) be a unitary representation of a compact Lie group \(K\) with Lie algebra \(\mathfrak k\). This series of talks will be devoted to some recent developments based on relations between the following three classical notions. \n\nThe ring of -invariant polynomials \(\mathbb C[V]^K\) is finitely generated by homogeneous elements\, by a theorem of Hilbert\, but the proof is notoriously nonconstructive. The degrees of a minimal set of generators are canonically determined by \(f\)\, and will be the focus of the discussion.\nThe \(K\)-equivariant momentum map \(\mu:\mathbb P(V)\to \mathfrak k^*\) associated to the Fubini-Study form encodes in its image properties of the invariant ring \(\mathbb C[V]^K\) and the \(K\)-module structure of the entire polynomial ring \(\mathbb C[V]\)\, due to theorems of Mumford and Brion. While many general properties of momentum images have been established\, explicit descriptions remain unknown in many cases south for in physics and quantum information theory.\nProjective geometry of complex \(K\)-orbits in \(\mathbb P(V)\); their fundamental forms\, osculating varieties and secant varieties.\n\nGeneral relations between the first two topics are well established\, even in a more general context. There are also well known relations between invariant theory and projective geometry\, but secant varieties have only recently been brought to the discussion and are subject of current interest. \nAfter introducing the basic notions\, I will derive some properties of momentum images related to fundamental forms and osculating varieties\, as well as a lower bound on the minimal positive degree of a homogeneous invariant\, derived using secant varieties. At the end I will present a class of homogeneous projective varieties\, characterized by a special property of their secant varieties\, where the relations between the above three concepts take a particularly pristine form. \nhttps://icms.bg/invariant-theory-homogeneous-projective-varieties-and-momentum-maps-course-by-valdemar-tsanov/ \n 
URL:https://math.bas.bg/event/%d1%81%d0%b5%d0%bc%d0%b8%d0%bd%d0%b0%d1%80-%d0%bd%d0%b0-%d0%bc%d1%86%d0%bc%d0%bd-10/
LOCATION:Институт по математика и информатика – БАН\, Block 8\, 1113 БАН IV км.\, София\, Bulgaria
CATEGORIES:Редовен семинар
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Sofia:20231114T140000
DTEND;TZID=Europe/Sofia:20231114T153000
DTSTAMP:20260507T082651
CREATED:20231110T170235Z
LAST-MODIFIED:20231110T170235Z
UID:15406-1699970400-1699975800@math.bas.bg
SUMMARY:Семинар по Приложна математика
DESCRIPTION:How log-concavity fought lottery frauds in Florida and what it did after winning\nДокладчик: Дмитри Карп\nДата: 14.11.2023 г.\nЧас: 14:00 ч.\nМясто: Зала 503 на ИМИ-БАН \nРезюме: In the talk I will first discuss the log-concavity in parameters of the normalized beta function (which represents the cumulative distribution function of beta distributed random variable) that has been used recently in an investigation of lottery frauds in Florida.  I will then present some related  properties of incomplete beta function and proceed to general log-concavity problems and their particular cases motivated by various problems in statistics\, probability and analysis. \nФейсбук страница на семинара: Семинар по Приложна математика
URL:https://math.bas.bg/event/%d1%81%d0%b5%d0%bc%d0%b8%d0%bd%d0%b0%d1%80-%d0%bf%d0%be-%d0%bf%d1%80%d0%b8%d0%bb%d0%be%d0%b6%d0%bd%d0%b0-%d0%bc%d0%b0%d1%82%d0%b5%d0%bc%d0%b0%d1%82%d0%b8%d0%ba%d0%b0-7/
LOCATION:Институт по математика и информатика – БАН\, Block 8\, 1113 БАН IV км.\, София\, Bulgaria
CATEGORIES:Редовен семинар
ORGANIZER;CN="%D0%98%D0%BD%D1%81%D1%82%D0%B8%D1%82%D1%83%D1%82%20%D0%BF%D0%BE%20%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0%20%D0%B8%20%D0%B8%D0%BD%D1%84%D0%BE%D1%80%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0%20-%20%D0%91%D0%90%D0%9D":MAILTO:office@math.bas.bg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Sofia:20231114T161500
DTEND;TZID=Europe/Sofia:20231114T173000
DTSTAMP:20260507T082651
CREATED:20231110T160109Z
LAST-MODIFIED:20231110T160109Z
UID:15397-1699978500-1699983000@math.bas.bg
SUMMARY:Национален колоквиум по математика
DESCRIPTION:СЪЮЗ НА МАТЕМАТИЦИТЕ В БЪЛГАРИЯ\n\nИНСТИТУТ ПО МАТЕМАТИКА И ИНФОРМАТИКА – БАН \n\n\n\nНАЦИОНАЛЕН КОЛОКВИУМ ПО МАТЕМАТИКА\n\n​Поредната сбирка на Колоквиума ще се състои на 14 ноември 2023 г. (вторник)  от 16:15 часа в Заседателната зала на ИМИ – БАН. Доклад на тема:\n\nArcs of High Divisibility and Their Applications to Coding Theory\nще изнесе проф. дмн Иван Ланджев\,\nИнститут по матем​атика и информатика\, Българска академия на науките. \n\n\n​Резюме
URL:https://math.bas.bg/event/%d0%bd%d0%b0%d1%86%d0%b8%d0%be%d0%bd%d0%b0%d0%bb%d0%b5%d0%bd-%d0%ba%d0%be%d0%bb%d0%be%d0%ba%d0%b2%d0%b8%d1%83%d0%bc-%d0%bf%d0%be-%d0%bc%d0%b0%d1%82%d0%b5%d0%bc%d0%b0%d1%82%d0%b8%d0%ba%d0%b0-26/
LOCATION:Институт по математика и информатика – БАН\, Block 8\, 1113 БАН IV км.\, София\, Bulgaria
CATEGORIES:Редовен семинар
ORGANIZER;CN="%D0%A1%D1%8A%D1%8E%D0%B7%20%D0%BD%D0%B0%20%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D1%86%D0%B8%D1%82%D0%B5%20%D0%B2%20%D0%91%D1%8A%D0%BB%D0%B3%D0%B0%D1%80%D0%B8%D1%8F":MAILTO:smb.sofia@gmail.com
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