Съвместна сбирка на семинара на МЦМН и семинара "Алгебра и Логика" в ИМИ, София, ще се проведе идния вторник, с доклад на Георги Томанов, както следва. Вторник, 29-ти април, 16:00 часа, зала 403 на ИМИ-БАН. Георги Томанов, Université Claude Bernard, Lyon 1. Group action on homogeneous spaces and applications in number theory Abstract: Many longstanding conjectures and problems in number theory can be reformulated in terms of group actions on homogeneous spaces. This reformulation allows them to be tackled using, alongside deep methods from algebra and algebraic geometry, powerful tools from ergodic theory and dynamical systems. An example of the effectiveness of this approach is Margulis's groundbreaking proof of the Oppenheim conjecture (formulated in 1929) concerning the values of quadratic forms at integer points. In this talk, [...]

Следващата сбирка на Семинара по геометрия на МЦМН ще се проведе в сряда, 30 април 2025 г. от 16:00 ч. в зала 403 и онлайн в Zoom: Доклад на тема Binary Quadratic Forms and Conway’s Topographs (Lecture 1 of 3) ще изнесе Nikita Kalinin, Guangdong Technion Israel Institute of Technology. Следващите две лекции ще бъдат на 07.05.2025 и 14.05.2025 от 16:00 ч. Abstract: Binary quadratic forms are as elementary as they are mysterious—much like prime numbers. In 1997, John Conway introduced topographs, a powerful geometric tool that provides a geometric visualization of binary quadratic forms and their values. These lectures will explore how topographs, combined with telescoping summation techniques, yield elegant formulas — some with intuitive geometric interpretations. For instance, consider the following result: Let [...]

Дата: 11.04.2025 г., 16:00 ч. Място: Зала 403, ИМИ - БАН Докладчик: Felipe Espreafico Guelerman, Sorbonne Université - Paris Доклад: On Motivic and Arithmetic Donaldson-Thomas invariants Допълнителна информация: https://icms.bg/category/icms-seminar/ Резюме. Aiming to understand the relation to other "refined invariants", and especially their possible interpretation in quantum theory, we explain how to obtain a quadratic, A1-version of Donaldson-Thomas invariants from the motivic refinements first introduced in Kontsevich-Soibelman. Following ideas from Behrend, Bryan and Szendroi, we provide predictions for these invariants in a few simple examples, mainly the computation of DT invariants of A3. Our main goal is to draw relationships with the literature, including works of Levine, Denef and Loser, Azouri, Pepin-Lehaulleur, Srinivas among others. We begin with a brief introduction to A1-enumerative geometry and [...]

Дата: 27.03.2025 г., 16:00 ч. Място: Зала 403, ИМИ - БАН Докладчик: Luis Ugarte, University of Zaragoza, Spain Доклад: Complex structures on Lie algebras and its application to the Hull-Strominger system Допълнителна информация: https://icms.bg/category/icms-seminar/ Резюме. In this talk we will explain the role that the Lie algebras play in the construction of 6-dimensional compact quotient spaces M=G/Γ, where Γ is a lattice, endowed with an invariant complex structure with holomorphically trivial canonical bundle.We will use the approach of stable forms in six dimensions to provide a classification of unimodular Lie algebras admitting a complex structure with non-zero closed (3,0)-form. Some of these spaces can be equipped with balanced Hermitian metrics and they provide invariant solutions of the Hull-Strominger system, even with non-flat connection on [...]

Дата: 25.03.2025 г., 14:00 ч. Място: Зала 403, ИМИ - БАН Докладчик: Михаил Школников, ИМИ - БАН Доклад: Affine distance function Допълнителна информация: https://icms.bg/category/icms-seminar/ Резюме. Affine geometry is sometimes described as "what remains of Euclidean geometry when distances are forgotten". In this talk, I will report on a very recent discovery of an affine-invariant notion, which may be viewed as a distance from a point inside a convex domain to its boundary. This new concept stems from a suggestion of Conan Leung, who proposed to average the canonical tropical series, a fundamental notion of tropical optics, over the manifold of all tropical structures of fixed covolume on the given affine space. Very little of what we (Nikita Kalinin, Ernesto Lupercio and me) currently know, [...]

Дата: 11.02.2025 г., 14:00 ч. Място: Зала 403, ИМИ - БАН Докладчик: Sergey Favorov, Department of Pure Mathematics, Kharkov National University, Ukraine Доклад: Fourier quasicrystals and their generalizations, zeros of Dirichlet series, other almost periodic objects Допълнителна информация: https://icms.bg/fourier-quasicrystals-and-their-generalizations-zeros-of-dirichlet-series-other-almost-periodic-objects-icms-seminar-talk-by-sergey-favorov/ Резюме. A complex measure \mu on a d -dimensional Euclidean space is a crystalline measure (CM) if it is the temperate distribution, its distributional Fourier transform \hat\mu is also a measure, and supports of \mu and \hat\mu are discrete (locally finite); \mu is a Fourier quasicrystal (FQ) if, in addition, |\mu| and |\hat\mu| are also temperate distributions. For example, if \mu_0 is the sum of the unit masses at all points with integer coordinates, then by Poisson’s [...]

Дата: 04.02.2025 г., 14:00 ч. Място: Зала 403, ИМИ - БАН Докладчик: Мирослав Георгиев, Институт по математика и информатика, Българска академия на науките Доклад: Yukawa regulators in electrodynamics: Exact approach to the self-energy and anomalous g-factor Допълнителна информация: https://icms.bg/yukawa-regulators-in-electrodynamics-exact-approach-to-the-self-energy-and-anomalous-g-factor-icms-seminar-talk-by-miroslav-georgiev/ Резюме. In the present talk, we will discuss the prospect of electrodynamics in quantifying the self-interaction of a non-composite charged particle. We will demonstrate that under the consideration of unique to the particle Yukawa cut-offs the radial singularity in corresponding electromagnetic field potentials’ is removed allowing the classical theory to admit exact solutions for the particle’s self-energy and anomalous g-factor. Highly accurate results for the electron’s and muon’s anomalous g-factor will be presented, with calculated values matching the most recent measurements reported in the literature [...]

Дата: 14.01.2025 г., 14:00 ч. Място: Зала 403, ИМИ - БАН Докладчик: Jean-Pierre Gazeau от Université Paris-Cité Доклад: Regularized Quantum Motion in a Bounded Set: Hilbertian Aspects Допълнителна информация: https://icms.bg/regularized-quantum-motion-in-a-bounded-set-hilbertian-aspects-talk-by-jean-pierre-gazeau/ Резюме. It is well known that the momentum operator canonically conjugated to the position operator for a particle confined within a bounded interval of the line (with Dirichlet boundary conditions) is not essentially self-adjoint, as it possesses a continuum of self-adjoint extensions. In this talk, we demonstrate that essential self-adjointness can be restored by symmetrically weighting the momentum operator with a positive bounded function that approximates the indicator function of the given interval. This weighted momentum operator arises naturally from a similarly weighted classical momentum through the Weyl-Heisenberg covariant integral quantization of functions or distributions. Reference: [...]