Следващата сбирка на Семинара по геометрия на МЦМН ще се проведе в сряда, 7 февруари 2024 г. от 16:00 ч. в зала 403 и онлайн в Zoom: Доклад на тема Introduction to curve counting ще изнесе Михаил Школников, ИМИ - БАН. Zoom link: https://us02web.zoom.us/j/83740034721?pwd=VnBtcVpGUktscHQ4a09jZkNZTURyZz09 Abstract: This talk is intended as a very gentle introduction to the classical subject of enumerative geometry concerned with problems of counting algebraic curves with prescribed properties. In the realm of classical planimetry, we know that there exists a single circle passing through a collection of three points, provided that these points are generic. Here “generic” simply means that the points are not collinear, i.e. don’t belong to the same line but could refer to some other open condition in [...]

Дата: 08.02.2024 г., 14:00 ч. Място: Зала 403, ИМИ - БАН Докладчик: Paul Horja, University of Miami, USA Доклад: A categorical view of singularity theory II Допълнителна информация: https://icms.bg/a-categorical-view-of-singularity-theory-i-and-ii-talks-by-paul-horja/ Резюме. The mirror symmetry phenomenon was discovered by string theorists more than thirty years ago as an equivalence of two physical theories associated with very different geometries. The categorical point of view on this remarkable conjecture was famously introduced by M. Kontsevich in his 1994 ICM talk. As it became clear over time, homological mirror symmetry provides new approaches to many topics in symplectic and algebraic geometry. In these two talks, I will present a brief overview of the conjecture as well as some results inspired by mirror symmetry and obtained in joint work with [...]

Дата: 06.02.2024 г., 14:00 ч. Място: Зала 403, ИМИ - БАН Докладчик: Paul Horja, University of Miami, USA Доклад: A categorical view of singularity theory I Допълнителна информация: https://icms.bg/a-categorical-view-of-singularity-theory-i-and-ii-talks-by-paul-horja/ Резюме. The mirror symmetry phenomenon was discovered by string theorists more than thirty years ago as an equivalence of two physical theories associated with very different geometries. The categorical point of view on this remarkable conjecture was famously introduced by M. Kontsevich in his 1994 ICM talk. As it became clear over time, homological mirror symmetry provides new approaches to many topics in symplectic and algebraic geometry. In these two talks, I will present a brief overview of the conjecture as well as some results inspired by mirror symmetry and obtained in joint work with [...]

Следващата сбирка на Семинара по геометрия на МЦМН ще се проведе в сряда, 31 януари 2024 г. от 16:00 ч. в зала 403 и онлайн в Zoom: Доклад на тема Derived Deformation Theory and Formal Moduli Problem ще изнесе Инди Чин, МЦМН и ИМИ - БАН. Zoom link: https://us02web.zoom.us/j/83740034721?pwd=VnBtcVpGUktscHQ4a09jZkNZTURyZz09 Abstract: Derived deformation theory studies the formal neighborhoods of moduli spaces. The classical work of Kodaira-Spencer on deformation of complex manifolds tells that the dg Lie algebra A^(0,*)(X,TX) controls the deformations of the complex manifold. The example illustrates the following general principle: A dg Lie algebra gives rise to a deformation functor by considering the  Maurer-Cartan elements of the dg Lie algebra tensoring with the maximal ideal of an Artin local ring. This idea is explored by [...]

Дата: 30.01.2024 г., 14:00 ч. Място: Зала 403, ИМИ - БАН Докладчик: Владимир Митанкин, ИМИ - БАН Доклад: Density of Hasse failures for diagonal affine cubic surfaces Допълнителна информация: https://icms.bg/density-of-hasse-failures-for-diagonal-affine-cubic-surfaces-a-talk-by-vladimir-mitankin/ Резюме. А question of Mordell asks which integers are the sum of three cubes provided that there are no local obstructions to that. While Mordell’s question seems out of reach with the current machinery, it is widely believed that every integer not congruent to 4 or 5 mod 9 is a sum of three integral cubes. If, instead of the sum of three cubes, a general ternary cubic is considered, local conditions no longer suffice for solubility, i.e. the integral Hasse principle may fail. In this talk we shall apply the integral version of the [...]

Следващата сбирка на Семинара по геометрия на МЦМН ще се проведе в сряда, 24 януари 2024 г. от 16:00 ч. в зала 403 и онлайн в Zoom: Доклад на тема Introduction to Derived Algebraic Geometry and deformation theory ще изнесе Инди Чин, ИМИ - БАН. Zoom link: https://us02web.zoom.us/j/83740034721?pwd=VnBtcVpGUktscHQ4a09jZkNZTURyZz09

Дата: 16.01.2024 г., 14:00 ч. Място: Зала 403, ИМИ - БАН Докладчик: Carlos Varea (Universidade Tecnológica  Federal do Paraná - Campus Cornélio Procópio, Brazil) Доклад: The H-flux on flag manifolds generated by infinitesimal T-duality Допълнителна информация: https://icms.bg/the-h-flux-on-flag-manifolds-generated-by-infinitesimal-t-duality-talk-by-carlos-varea/ Резюме. 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 joint [...]

На 18 януари 2024 г. (четвъртък) от 13:00 часа в зала 403 на ИМИ-БАН и онлайн чрез платформата zoom ще се проведе съвместно заседание на Семинара на секция „Алгебра и логика” и Семинара на Международния център по математически науки към ИМИ-БАН. Доклад на тема Nilpotent algebras, groups and beyond ще изнесе Yuri Bahturin (Memorial University of Newfoundland, Canada) (joint work with Alexander Olshanskii). Абстракт: We study various correspondences between finite-dimensional nilpotent algebras and (quasi)groups similar to those given by the circle product in the case of associative algebras or by the Baker-Campbell-Hausdorff formulas in the the case of Lie algebras or their generalizations. In the particular case of Malcev's correspondence, we obtain some new results about groups using Lie algebras and vice versa. Линк към [...]

Дата: 11.01.2024 г., 14:00 ч. Място: Зала 403, ИМИ - БАН Докладчик: д-р Антони Рангачев, ИМИ - БАН Доклад: The Milnor number of a smoothable curve Допълнителна информация: https://icms.bg/the-milnor-number-of-a-smoothable-curve-talk-by-antony-rangachev/ Резюме. 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.  

Дата: 09.01.2024 г., 14:00 ч. Място: Зала 403, ИМИ - БАН Докладчик: д-р Антони Рангачев, ИМИ - БАН Доклад: Stratified Morse theory and the critical locus of a linear functional Допълнителна информация: https://icms.bg/stratified-morse-theory-and-the-critical-locus-of-a-linear-functional-talk-by-antony-rangachev/ Резюме. 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.