На 6 юни 2025 г. (петък) от 12:30 часа в зала 578 на ИМИ и онлайн чрез платформата zoom ще се проведе хибридно заседание на семинара по „Алгебра и логика”. Доклад на тема: Holographic probe branes and artificial neural networks ще изнесе Веселин Филев (ИМИ-БАН). Резюме: In holography, flavour probe branes are used to introduce fundamental matter to the AdS/CFT correspondence. At a technical level, the probes are described by extremizing the DBI action and solving the Lagrange–Euler equations of motion. I will report on applications of artificial neural networks that allow direct minimization of the regularized DBI action (interpreted as a free energy) without the need to derive and solve the equations of motion. I will consider, as examples, magnetic catalysis of chiral [...]

На 16 май 2025 г. (петък) от 13:00 часа в зала 503 на ИМИ и онлайн чрез платформата zoom ще се проведе хибридно заседание на семинара по „Алгебра и логика”. Доклад на тема: Grätzer-Schmidt Theorem in arithmetical transfinite recursion ще изнесе Soowhan Yoon (American University in Bulgaria). Abstract: We assess the reverse mathematical strength of the Grätzer-Schmidt theorem (GS) as a principle in second order arithmetic. The theorem GS was studied in an article by Katie Brodhead, Mushfeq Khan, Bjørn Kjos-Hanssen, William A. Lampe, Paul Kim Long V. Nguyen, and Richard A. Shore, where they establish the provability of GS in Π11 Comprehension (Π11-CA0) and its restrictive variant GSD in arithmetical comprehension (ACA0). It will be shown that the arithmetical transfinite recursion (ATR0) is sufficient to prove [...]

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, 14:00 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 [...]

На 25 април 2025 г. (петък) от 13:00 часа в зала 578 на ИМИ ще се проведе заседание на семинара по „Алгебра и логика”. Доклад на тема: Hilbert scheme of smooth projective curves and some easy examples ще изнесе Changho Keem (Seoul National University, South Korea). Abstract: Hilbert scheme is a parameter space for a family of projective algebraic varieties sharing a given fixed Hilbert polynomial.  In this talk, we will discuss the following topics concerning the Hilbert scheme of smooth projective algebraic curves. 1. Irreducibility problem of the restricted Hilbert scheme of curves. 2. Some easy examples of reducible Hilbert schemes inside or outside the Brill-Noether range. 3. The existence of more than expected dimensional components whose image under the moduli map has small codimension [...]

На 28 март 2025 г. (петък) от 13:00 часа в зала 578 на ИМИ и онлайн чрез Zoom ще се проведе хибридно заседание на семинара по „Алгебра и логика”. Доклад на тема: Graded algebras that are the sum of two homogeneous subalgebras ще изнесе Пламен Кошлуков (State University of Campinas, Brazil). Абстракт. Let A be an algebra over a field F, graded by a group G, and let B and C be two homogeneous subalgebras of A such that A=B+C. We study the following problem: If B and C satisfy graded identities, does the same also hold for A? The analogous problem for algebras without any grading was proposed in 1994 by Beidar and Mikhalev; in implicit form it appeared in a paper by O. Kegel, in 1963. Several particular cases were [...]

На 14 март 2025 г. (петък) от 13:00 часа в зала 578 на ИМИ и онлайн чрез Zoom ще се проведе хибридно заседание на семинара по „Алгебра и логика”. Доклад на тема: Protection Against Noise for a Type of Quantum Computation ще изнесе Валентин Илиев (ИМИ-БАН). Абстракт. In this presentation we establish necessary and sufficient conditions for some pairs of quantum logic gates which operate on one qubit to be protected against crosstalk. More precisely, it is devoted to the protection against noise for measurement-based quantum computation. We use the notions of (in)dependence of two events in an appropriate classical probability space and the related informational (in)dependence.   Линк към zoom-стаята на семинара: Https://us02web.zoom.us/j/85137375021?pwd=RE5QczdFTE1xL1R6MnI2b1lkcGczQT09 Поканват се всички желаещи да присъстват. От секция „Алгебра и логика” [...]

На 21 февруари 2025 г. (петък) от 13:00 часа в зала 578 на ИМИ ще се проведе присъствено заседание на семинара по „Алгебра и логика”. Доклад на тема: Classification of C*-algebras through the lens of Cartan subalgebras ще изнесе Ali Raad (Американски университет в България). Абстракт. C*-algebras were introduced in the last century following various attempts to mathematically formalize the foundations of quantum mechanics. As such they encapsulate the study of noncommutative topology, as every C*-algebra is an algebra of bounded operators on some Hilbert space. Over the years there has been a significant attempt to classify C*-algebras by an invariant consisting of K-theoretic and tracial data. A recent breakthrough result has shown that every classifiable C*-algebra has a distinguished Abelian subalgebra called a Cartan [...]

На 22 ноември 2024 г. (петък) от 13:00 часа в зала 578 на ИМИ ще се проведе присъствено заседание на семинара по „Алгебра и логика”. Доклад на тема: On Köthe’s normality question for locally finite-dimensional central division algebras ще изнесе Иван Чипчаков, ИМИ - БАН. Абстракт. This talk considers Köthe's question of whether every associative locally finite-dimensional (abbr., LFD) central division algebra R over a field K is a normally locally finite (abbr., NLF) algebra over K, that is, whether every nonempty finite subset Y of R is contained in a finite-dimensional central K-subalgebra RY of R. It shows that the answer to the posed question is negative if K is a purely transcendental extension of infinite transcendence degree over an algebraically closed field k. On the other hand, central [...]

На 7 юни 2024 г. (петък) от 12:30 часа в зала 503 на ИМИ ще се проведе присъствено заседание на семинара по „Алгебра и логика”. Доклад на тема: Some Properties and Applications of Kloosterman Sums on Finite Fields ще изнесе Любомир Борисов, ИМИ - БАН. Абстракт Поканват се всички желаещи да присъстват. От секция „Алгебра и логика” на ИМИ – БАН http://www.math.bas.bg/algebra/seminarAiL/ ============================== =====================

На 12 април 2024 г. (петък) от 13:00 часа ще се проведе дистанционно заседание на семинара по „Алгебра и логика”. Доклад на тема: On an Aspect of Second Quantum Revolution ще изнесе Валентин Илиев, ИМИ - БАН. Абстракт. The 2022 Nobel Prize in Physics has been awarded to Alain Aspect, John Clauser, and Anton Zeilinger for their work in Quantum Theory. Mass media called this event part of second quantum revolution which includes mainly quantum computing and other super-technologies. Here we discuss Alain Aspect's version of Einstein-Podolsky-Rosen thought experiment and show that there exists an internal dependence of the simultaneous measurements made by the two pairs of linear polarizers operated in each leg of the apparatus during this experiment. The corresponding Shannon-Kolmogorov information flow [...]