Time: November 23, 2023, 2:00 pm Place: Room 403, IMI - BAS Speaker: Peter Dalakov, IMI-BAS Course title: Invariant theory, homogeneous projective varieties, and momentum maps Abstract: 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. The ring of K -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. The K -equivariant momentum map \mu:\mathbb P(V)\to \mathfrak [...]

Time: November 21, 2023, 2:00 pm Place: Room 403, IMI - BAS Speaker: Peter Dalakov, IMI-BAS Course title: Invariant theory, homogeneous projective varieties, and momentum maps Abstract: 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. The ring of K -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. The K -equivariant momentum map \mu:\mathbb P(V)\to \mathfrak [...]

Time: November 16, 2023, 2:00 pm Place: Room 403, IMI - BAS Speaker: Peter Dalakov, IMI-BAS Course title: Invariant theory, homogeneous projective varieties, and momentum maps Abstract: 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. The ring of K -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. The K -equivariant momentum map \mu:\mathbb P(V)\to \mathfrak [...]

Time: November 14, 2023, 2:00 pm Place: Room 403, IMI - BAS Speaker: Peter Dalakov, IMI-BAS Course title: Invariant theory, homogeneous projective varieties, and momentum maps Abstract: 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. The ring of K -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. The K -equivariant momentum map \mu:\mathbb P(V)\to \mathfrak [...]

Time: November 6, 2023, 2:00 pm Place: Room 403, IMI - BAS Speaker: Peter Dalakov, IMI-BAS Course title: Introduction to Projective Structures and Opers Abstract: 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. https://icms.bg/introduction-to-projective-structures-and-opers/  

Time: November 2, 2023, 2:00 pm Place: Room 403, IMI - BAS Speaker: Peter Dalakov, IMI-BAS Course title: Introduction to Projective Structures and Opers Abstract: 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. https://icms.bg/introduction-to-projective-structures-and-opers/  

Time: October 31, 2023, 2:00 pm Place: Room 403, IMI - BAS Speaker: Peter Dalakov, IMI-BAS Course title: Introduction to Projective Structures and Opers Abstract: 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. https://icms.bg/introduction-to-projective-structures-and-opers/  

Time: October 30, 2023, 2:00 pm Place: Room 403, IMI - BAS Speaker: Peter Dalakov, IMI-BAS Course title: Introduction to Projective Structures and Opers Abstract: 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. https://icms.bg/introduction-to-projective-structures-and-opers/