На 16 септември 2022 г. (петък) от 14:00 ч. ще се проведе дистанционно заседание на семинара по „Алгебра и логика”. Доклад на тема: Almost Prime Ideal and Almost Prime Radical ще изнесе Alaa Abouhalaka (Çukurova University, Adana, Turkey). Абстракт. In this talk, we introduce the concept of almost prime (right) ideals in noncommutative rings and provide some equivalent definitions and new results. Also we introduce the concept of almost prime radical of an ideal. References: [1] M.S. Bhatwadekar, P. K. Sharma, Unique factorization and birth of almost primes, Comm. Algebra, 33(1), 43-49, (2005). [2] W.D. Blair, H. Tsutsui, Fully prime rings, Comm. Algebra, 22(13), 5389-5400, (1994).   Семинарът ще се проведе посредством платформата Zoom и всеки желаещ може да се присъедини като последва линка: [...]

На 9 септември 2022 г. (петък) от 13:00 ч. ще се проведе дистанционно заседание на семинара по „Алгебра и логика”. Доклад на тема: Timing delays in cyber-physical systems ще изнесе Naijun Zhan (Institute of Software Chinese Academy of Sciences ISCAS, China). Абстракт. With the rapid development of feedback control, sensor techniques and computer control, time delay has become an essential feature of cyber-physical systems (CPSs), underlying both the continuous evolution of physical plants and the discrete transition of computer programs, which may well annihilate the stability/safety certificate and control performance of CPSs. In the safety-critical context, automatic verification and synthesis methods addressing time-delay in CPSs should therefore abound. However, surprisingly, they do not, although time-delay has been extensively studied in the literature of mathematics [...]

На 19 август 2022 г. (петък) от 13:00 ч. в зала 578 на ИМИ - БАН ще се проведе хибридно заседание на семинара по „Алгебра и логика”. Доклад на тема: Examples of non-reduced components of the Hilbert Scheme of smooth projective curves using ruled surfaces ще изнесе Христо Илиев (АУБ и ИМИ-БАН). Абстракт. Let Id,g,r be the union of irreducible components of the Hilbert scheme whose general points represent smooth irreducible non-degenerate curves of degree d and genus g in Pr. Using a family of curves found on ruled surfaces over smooth curves of genus γ, we show that for γ ≥ 7 and g ≥ 6γ+5 the scheme I2g−4γ+1,g,g−3γ+1 acquires a non-reduced component D′ such that dim T[X′]D′ = dimD′ + 1 for [...]

На 29 юли 2022 г. (петък) от 13:00 ч. ще се проведе дистанционно заседание на семинара по „Алгебра и логика”. Доклад на тема: Modal Descriptive Complexity ще изнесе Петър Илиев (ИФС-БАН и ИМИ-БАН). Абстракт. The study of the descriptive complexity of a class of structures S relative to a class of formulae F from a logic L revolves around the question: what can we say about the definability of S with formulae from F? For example, we might want to know whether there is a formula from F defining S or, if not, whether there is a countably infinite sequence of F-formulae such that each formula from the sequence defines a subset of S and the union of all these subsets is the whole [...]

На 1 юли 2022 г. (петък) от 13:00 ч. ще се проведе дистанционно заседание на семинара по „Алгебра и логика”. Доклад на тема: On the parity of the coefficients of minimal polynomial of Kloosterman sums over Fp ще изнесе Любомир Борисов. Абстракт. Kloosterman sums over finite fields play an important role in "Algebraic Coding Theory" and "Cryptography". E.g., they are related to some families of algebraic codes (Melas, Kloosterman) and (hyper-)bent functions. Particularly, the divisibility properties of some quantities connected with the Kloosterman sums, e.g., of minimal polynomial coefficients and power moments, were also investigated (see, e.g., [1]; [2]). In this talk I shall present some results about the divisibility by 2 of the coefficients of minimal polynomials of the Kloosterman sums. [1] M. Moisio, [...]

На 24 юни 2022 г. (петък) от 13:00 ч. ще се проведе дистанционно заседание на семинара по „Алгебра и логика”. Доклад на тема: Dependent-Type Theory of Situated Information with Context Assessments ще изнесе Русанка Луканова. Абстракт. I shall introduce an enriched formal language of information that establishes propositions dependent on situations and types. The types can be basic or complex. Complex propositional types are defined recursively. The language supports structured data of situated information, which can be partial, parametric, and underspecified. Information can be associated with quantitative evaluations depending on situations. The formal terms can integrate propositional types of situated information with statistical and other quantitative evaluations. Structured content integrated with quantitative data facilitates development of new techniques for amalgamating logic representation of situated, propositional [...]

На 10 юни 2022 г. (петък) от 16:00 ч. ще се проведе дистанционно заседание на семинара по „Алгебра и логика”. Доклад на тема: Computing Eigenvectors of Symmetric Tridiagonals with the Correct Number of Sign Changes ще изнесе Plamen Koev (San José State University, USA). Абстракт. The symmetric tridiagonal eigenvector problem has been a central research topic in numerical linear algebra since its inception. Of the myriad of algorithms today, none is provably optimal and accurate at the same time. “Optimal” means, a subset of k eigenvectors is computed in O(kn) time. “Accurate” means that the computes eigenvectors are orthogonal and satisfy the typical relative gap error bound. In this talk, we focus our attention on a neglected oscillating property of the eigenvectors: the i-th eigenvector has [...]

На 20 май 2022 г. (петък) от 16:00 ч. ще се проведе дистанционно заседание на семинара по „Алгебра и логика”. Доклад на тема: Bootstrap percolation: merging operations for polytopes ще изнесе Ivailo Hartarsky (Université Paris-Dauhpine, PSL, France, visiting scholar at Instituto de Matemática Pura e Aplicada, Rio de Janeiro, Brazil). Абстракт. Bootstrap percolation is a group of statistical physics models intensively studied since the 1970s in mathematics, physics, computer science, as well as social sciences. They are cellular automata generalising the following paradigmatic example. Arbitrarily declare some sites of Z^2 initially infected. Iteratively, at each discrete-time round, additionally infect each site with at least 2 infected neighbours. The last decade has seen the accomplishment of a full classification of all such models into `universality [...]

На 13 май 2022 г. (петък) от 13:00 ч. ще се проведе дистанционно заседание на семинара по „Алгебра и логика”. Доклад на тема: A counterexample to the modular isomorphism problem ще изнесе Diego García-Lucas (Universidad de Murcia, Spain). Абстракт. The modular isomorphism problem asks whether the isomorphism type of the modular group algebra of a p-group G over a field of characteristic p determines the isomorphism type of G. It was explicitly mentioned in a survey by Richard Brauer in 1963, and was the only classical version of the isomorphism problem for group rings which had resisted a solution, though it received considerable attention. Several partial positive solutions were obtained imposing very strong conditions on the group G, for instance the one of being [...]

На 29 април 2022 г. (петък) от 16:00 ч. ще се проведе дистанционно заседание на семинара по „Алгебра и логика”. Доклад на тема: Images of multilinear polynomials on upper triangular matrices ще изнесе Thiago Castilho de Mello (Universidade Federal de São Paulo, Brazil). Резюме. Let f(x1, …, xm) be a polynomial in noncommutative variables over an infinite field K. If A is a K-algebra, it defines in a natural way a map Am → A. If the polynomial f is multilinear, the famous Lvov-Kaplansky conjecture asks whether the image of a multilinear polynomial on a matrix algebra is a vector subspace. Solutions to this problem are known only for n = 2 or m = 2 with partial results for m = 3 and n = 3. In this talk, we survey these results and [...]