Time: January 16, 2024, 2:00 pm Place: Room 403, IMI - BAS Speaker: Carlos Varea (Universidade Tecnológica  Federal do Paraná - Campus Cornélio Procópio, Brazil) Title: The H-flux on flag manifolds generated by infinitesimal T-duality Further information: https://icms.bg/the-h-flux-on-flag-manifolds-generated-by-infinitesimal-t-duality-talk-by-carlos-varea/ Abstract. In this talk we present a new correspondence for pairs (\mathbb{F},H) formed by a flag manifold \mathbb{F} together with an $H$-flux on \mathbb{F} . Given its role within our correspondence, infinitesimal T -duality may be viewed as a source of H -flux, in the sense that it contributes towards taking fluxless pairs (\mathbb{F},0) to pairs (\mathbb{F}^\vee, H^\vee) carrying nontrivial flux H^\vee\neq 0 . We also illustrate how our correspondence exchanges complex structures with symplectic ones up to B -transformations. This is a [...]

Time: January 11, 2024, 2:00 pm Place: Room 403, IMI - BAS Speaker: Antoni Rangachev, IMI-BAS Title: The Milnor number of a smoothable curve Further information: https://icms.bg/the-milnor-number-of-a-smoothable-curve-talk-by-antony-rangachev/ Abstract. In this talk I will derive an algebraic formula for the Milnor number of a smoothable complex analytic curve singularity X by relating it to the Euler characteristic of its smoothing, which in turn I will relate to the multiplicity of the Jacobian ideal of X and and the multiplicity of X at its singular point. If time permits I will discuss generalizations to higher dimensions. This is a report on a joint work with Gaffney and Bengus-Lasnier.  

Time: January 9, 2024, 2:00 pm Place: Room 403, IMI - BAS Speaker: Antoni Rangachev, IMI-BAS Title: Stratified Morse theory and the critical locus of a linear functional Further information: https://icms.bg/stratified-morse-theory-and-the-critical-locus-of-a-linear-functional-talk-by-antony-rangachev/ Abstract. In this talk I will use stratified Morse theory to relate the number of critical points of a generic linear functional on a complex analytic manifold M to the Euler characteristics of M and a generic hyperplane slice of M.

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 [...]