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 [...]

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 [...]

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 [...]

На 23 февруари 2024 г. (петък) от 13:00 часа ще се проведе дистанционно заседание на семинара по „Алгебра и логика”. Доклад на тема: Invariant subalgebras of the rational Cherednik algebra ще изнесе Niall Hird (University of Glasgow, UK). Абстракт. The rational Cherednik algebra is a degeneration of the double affine Hecke algebra and an object of interest to many representation theorists, it also has strong connections to integrable systems. In my talk I will discuss two subalgebras that arise from considering the invariants of the action of reductive subgroups of the special linear group. In particular we will examine the centres of these invariant subalgebras and compare with the algebra of invariants of the centre of the entire rational Cherednik algebra under the same [...]

На 8 януари 2024 г. (понеделник) от 13:00 часа в зала 578 на ИМИ-БАН и онлайн чрез платформата zoom ще се проведе хибридно заседание на семинара по „Алгебра и логика”. Доклад на тема: On the exceptional series and its siblings ще изнесе Bruce Westbury (retired from University of Warwick, UK). Абстракт. The exceptional series is the following series of eight simple Lie algebras: A1, A2, G2, D4, F4, E6, E7, E8 Consider each Lie algebra, g, as a representation of the group Aut(g). Then the centraliser algebras of the first five tensor powers of g have common structure. First, they have the same branching rules. We introduce a parameter so that the exceptional series is a set of eight points on a line. Then the [...]