Дата: 12.03.2024 г., 14:00 ч. Място: Зала 403, ИМИ - БАН Докладчик: Morgan Brown  (University of Miami) Доклад: The Cox ring perspective on birational geometry Допълнителна информация: https://icms.bg/the-cox-ring-perspective-in-birational-geometry-talk-by-morgan-brown/ Резюме. The Mori program for birational classification of algebraic varieties attempts to classify algebraic varieties by producing canonical models, polarized by the canonical class. This is accomplished through a series of algebraic surgery operations, such as flips, flops, and divisorial contractions. A complementary viewpoint is that of the total coordinate ring or Cox ring. Here birational maps are understood by looking at the totality of all linear series on the variety, endowed with a ring structure directly analogous to that of the homogeneous coordinate ring of a projective variety. I will give an overview of how […]

Дата: 14.03.2024 г., 14:00 ч. Място: Зала 403, ИМИ - БАН Докладчик: Morgan Brown  (University of Miami) Доклад: Cox rings and characterization of toric varieties Допълнителна информация: https://icms.bg/the-cox-ring-perspective-in-birational-geometry-talk-by-morgan-brown/ Резюме. Recently Moraga and Svaldi proved a conjecture of Shokoruv, characterizing in the relative case toroidal morphisms as those which admit divisors with many components relative to the Picard rank. I will discuss the global version, proved in previous joint work with McKernan, Svaldi and Zong. The proof relies on characterizing the singularity type of the Cox ring, giving another example of the use of these invariants in birational geometry.

Сбирка на семинара "Математически основи на информатиката" ще се проведе във Велико Търново на 18 март (понеделник) от 16:30 часа в зала 401 на корпус 4 на ВТУ. Доклад на тема LCD Codes over Mixed Alphabets ще изнесе Maryam Bajalan, ИМИ - БАН. Резюме: In this presentation, we describe the structural properties of (Galois) linear complementary dual codes over mixed alphabets arising from finite chain rings. Our focus centres on providing a comprehensive characterization, outlining the conditions under which a given code falls into this category and it is Galois invariant. This leads to the study of the Gray image of FpFp-linear codes, where p ∈ {2,3} and θ ≠ θ2 = 0 , that provides Fp-linear complementary dual codes. Join Zoom Meeting https://us05web.zoom.us/j/87139062405?pwd=OytyS4AVwUy9U0Ok9hbW9tivGfFauR.1 […]

Дата и час: 19.03.2024 г., сряда, 16:00 ч. Място: изцяло в Zoom Лектор: Веселин Петков (Université Bordeaux) Доклад: Dynamical zeta function for billiard flow Абстракт: We will present briefly the connection between Riemann zeta function, Ruellle zeta function and dynamical zeta function. The last one is related to the billiard flow for the union D \subset R^d of a finite collection of pairwise disjoint strictly convex compact obstacles. Let \mu_j \in C, \Im \mu_j > 0 be the resonances of the Laplacian in the exterior of D with Neumann or Dirichlet boundary condition on \partial D. For d odd, u(t) = \sum_j e^{i |t| \mu_j} is a distribution in \mathcal{D}'(R \setminus \{0\}) and the Laplace transforms of the leading singularities of u(t) yield the […]

Следващата сбирка на Семинара по геометрия на МЦМН ще се проведе в сряда, 20 март 2024 г. от 16:00 ч. в зала 403: Доклад на тема Ellipsoid superpotentials: obstructing symplectic embeddings by singular algebraic curves ще изнесе Григори Михалкин, Женевски университет. Abstract: How singular can be a local branch of a plane algebraic curve of a given degree d? A remarkable series of real algebraic curves was constructed by Stepan Orevkov. It is based on even-indexed numbers in the Fibonacci series: a degree 5 curve with a 13/2 cusp, a degree 13 curve with a 34/5-cusp, and so on. We discuss this and other series of algebraic curves in the context of the problem of symplectic packing of an ellipsoid into a ball, with […]

На 22 март 2024 г. (петък) от 13:00 часа ще се проведе дистанционно заседание на семинара по „Алгебра и логика”. Доклад на тема: On the uniqueness of maximal solvable extensions of nilpotent Lie algebras ще изнесе Bakhrom A. Omirov (Harbin Institute of Technologies, Harbin, China and Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, Uzbekistan). Абстракт. During the talk it will be shown that under certain condition an arbitrary complex finite-dimensional maximal extension of a nilpotent Lie algebra N is isomorphic to the semidirect sum of N and its maximal torus. A criterion of the completeness for a finite-dimensional solvable Lie algebra is established. Comparisons with some existing results will also be discussed. Линк към Zoom-стаята на семинара: https://us02web.zoom.us/j/85137375021?pwd=RE5QczdFTE1xL1R6MnI2b1lkcGczQT09 От секция „Алгебра и логика” на […]

On constructions of spherical codes Докладчик: д-р Константин Воробьов, ИМИ - БАН Дата: 27.03.2024 г. Час: 16:00 ч. Място: зала 503 Резюме: In this talk, we review various approaches to construct spherical codes with a given coding distance. We also propose a new approach that allows us to find new codes on spheres in small dimensions. In particular, we find a previously unknown kissing arrangement of 40 spheres in R^5.  

Следващата сбирка на Семинара по геометрия на МЦМН ще се проведе в сряда, 27 март 2024 г. от 16:00 ч. в зала 403: Доклад на тема Reading seminar of geometric Lubin-Tate theory ще изнесе Jiachang Xu, ИМИ - БАН. Abstract: This is reading seminar of geometry of Lubin-Tate theory, our goal is to understand the papers “M. J. Hopkins and B. H. Gross, Equivariant vector bundles on the Lubin-Tate moduli space” and “Ramero, Lorenzo On a class of étale analytic sheaves”. The first seminar we plan to go over the basis of deformation theory, formal group and necessary rigid geometry. Zoom link: https://us02web.zoom.us/j/83740034721?pwd=VnBtcVpGUktscHQ4a09jZkNZTURyZz09

На 29 март 2024 г. (петък) от 13:00 часа ще се проведе дистанционно заседание на семинара по „Алгебра и логика”. Доклад на тема: Generalized Definability of Discrete Time Interval-based Temporal Connectives ще изнесе Димитър Гелев, ИМИ - БАН. Абстракт. In Linear Temporal Logic with past (PLTL), expressive completeness implies that any first-order definable connective is also definable in the temporal language based on the Since and Until temporal operators. This is not the case about discrete time interval-based temporal logics with state-based semantics for the propositional variables. In this talk I prove the next best thing about the extension ITLNL of Moszkowski's discrete time propositional Interval Temporal Logic (ITL) by the neighbourhood modalities: given an interval-based connective # which admits a first-order definition, a star-free ITLNL defining formula for #(A1,...,Am) can be produced that […]