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DTSTART;TZID=Europe/Sofia:20231102T140000
DTEND;TZID=Europe/Sofia:20231102T153000
DTSTAMP:20260419T102220
CREATED:20231010T081045Z
LAST-MODIFIED:20231010T081045Z
UID:15128-1698933600-1698939000@math.bas.bg
SUMMARY:Семинар на МЦМН
DESCRIPTION:Дата: 02.11.2023 г.\, 14:00 ч. \nМясто: Зала 403\, ИМИ – БАН \nДокладчик: Петър Далаков\, ИМИ – БАН \nКурс: Introduction to Projective Structures and Opers \nРезюме: A complex projective structure on a Riemann surface is determined by an atlas\, whose transition functions are Moebius (fractional-linear) transformations. There are multiple   descriptions of these structures: as certain flat PGL_2-bundles\, as Sturm-Liouville operators\, as holomorphic connections on the (first) jet bundle of the dual of a theta-characteristic\, etc. This mini-course is an introduction to the fundamentals of projective structures\, accessible to students and non-specialists. We will also explore links to some classical geometric objects (such as quadratic differentials and Schwarzian derivatives)\, as well as some generalisations (G-opers) introduced by Beilinson and Drinfeld. \n\nIntroduction to Projective Structures and Opers\, course by Peter Dalakov \n\n  \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-8/
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:20231106T140000
DTEND;TZID=Europe/Sofia:20231106T153000
DTSTAMP:20260419T102220
CREATED:20231010T081237Z
LAST-MODIFIED:20231010T081237Z
UID:15132-1699279200-1699284600@math.bas.bg
SUMMARY:Семинар на МЦМН
DESCRIPTION:Дата: 06.11.2023 г.\, 14:00 ч. \nМясто: Зала 403\, ИМИ – БАН \nДокладчик: Петър Далаков\, ИМИ – БАН \nКурс: Introduction to Projective Structures and Opers \nРезюме: A complex projective structure on a Riemann surface is determined by an atlas\, whose transition functions are Moebius (fractional-linear) transformations. There are multiple   descriptions of these structures: as certain flat PGL_2-bundles\, as Sturm-Liouville operators\, as holomorphic connections on the (first) jet bundle of the dual of a theta-characteristic\, etc. This mini-course is an introduction to the fundamentals of projective structures\, accessible to students and non-specialists. We will also explore links to some classical geometric objects (such as quadratic differentials and Schwarzian derivatives)\, as well as some generalisations (G-opers) introduced by Beilinson and Drinfeld. \n\nIntroduction to Projective Structures and Opers\, course by Peter Dalakov \n\n  \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-9/
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:20260419T102220
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. \n\nInvariant theory\, homogeneous projective varieties\, and momentum maps\, course by Valdemar Tsanov \n\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:20231115T160000
DTEND;TZID=Europe/Sofia:20231115T173000
DTSTAMP:20260419T102220
CREATED:20231110T165607Z
LAST-MODIFIED:20231110T165607Z
UID:15402-1700064000-1700069400@math.bas.bg
SUMMARY:Семинар по геометрия на МЦМН
DESCRIPTION:Следващата сбирка на Семинара по геометрия на МЦМН\nще се проведе в сряда\, 15 ноември 2023 г. от 16:00 ч. в зала 403 и онлайн в Zoom:\n\nTopics in non-archimedean analytic geometry (I)\, \nby Jiachang Xu – International Center for Mathematical Sciences (ICMS – Sofia)\n\nZoom link:\n\nhttps://us02web.zoom.us/j/83740034721?pwd=VnBtcVpGUktscHQ4a09jZkNZTURyZz09
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%b3%d0%b5%d0%be%d0%bc%d0%b5%d1%82%d1%80%d0%b8%d1%8f-%d0%bd%d0%b0-%d0%bc%d1%86%d0%bc%d0%bd-2/
LOCATION:Институт по математика и информатика – БАН\, Block 8\, 1113 БАН IV км.\, София\, Bulgaria
CATEGORIES:Редовен семинар
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BEGIN:VEVENT
DTSTART;TZID=Europe/Sofia:20231116T140000
DTEND;TZID=Europe/Sofia:20231116T153000
DTSTAMP:20260419T102220
CREATED:20231010T091536Z
LAST-MODIFIED:20231010T091536Z
UID:15145-1700143200-1700148600@math.bas.bg
SUMMARY:Семинар на МЦМН
DESCRIPTION:Дата: 16.11.2023 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. \n\nInvariant theory\, homogeneous projective varieties\, and momentum maps\, course by Valdemar Tsanov \n\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-11/
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:20231121T140000
DTEND;TZID=Europe/Sofia:20231121T153000
DTSTAMP:20260419T102220
CREATED:20231010T091730Z
LAST-MODIFIED:20231010T091730Z
UID:15149-1700575200-1700580600@math.bas.bg
SUMMARY:Семинар на МЦМН
DESCRIPTION:Дата: 21.11.2023 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. \n\nInvariant theory\, homogeneous projective varieties\, and momentum maps\, course by Valdemar Tsanov \n\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-12/
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:20231122T160000
DTEND;TZID=Europe/Sofia:20231122T173000
DTSTAMP:20260419T102220
CREATED:20231121T164225Z
LAST-MODIFIED:20231121T164225Z
UID:15481-1700668800-1700674200@math.bas.bg
SUMMARY:Семинар по геометрия на МЦМН
DESCRIPTION:Следващата сбирка на Семинара по геометрия на МЦМН\nще се проведе в сряда\, 22 ноември 2023 г. от 16:00 ч. в зала 403 и онлайн в Zoom:\n\n\nTopics in non-archimedean analytic geometry (II)\n\nby Jiachang Xu – International Center for Mathematical Sciences (ICMS – Sofia)\n\nZoom link:\n\nhttps://us02web.zoom.us/j/83740034721?pwd=VnBtcVpGUktscHQ4a09jZkNZTURyZz09
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%b3%d0%b5%d0%be%d0%bc%d0%b5%d1%82%d1%80%d0%b8%d1%8f-%d0%bd%d0%b0-%d0%bc%d1%86%d0%bc%d0%bd-3/
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:20231123T140000
DTEND;TZID=Europe/Sofia:20231123T153000
DTSTAMP:20260419T102220
CREATED:20231010T091918Z
LAST-MODIFIED:20231010T091918Z
UID:15153-1700748000-1700753400@math.bas.bg
SUMMARY:Семинар на МЦМН
DESCRIPTION:Дата: 23.11.2023 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. \n\nInvariant theory\, homogeneous projective varieties\, and momentum maps\, course by Valdemar Tsanov \n\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-13/
LOCATION:Институт по математика и информатика – БАН\, Block 8\, 1113 БАН IV км.\, София\, Bulgaria
CATEGORIES:Редовен семинар
END:VEVENT
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