The next meeting of the Algebra and Logic Seminar will be held on October 21, 2022 (Friday) at 1:00 pm (UTC+2) online in Zoom. A talk on: Ranks and Presentations for Order-Preserving Transformations with One Fixed Point will be delivered by Jörg Koppitz (joint work with S. Worawiset). Abstract. We consider the semigroup (no monoid) of all order-preserving full transformations α on an n-element chain Xn = {1 < 2 …< n}, where p is the only fixed point in α, for some given p ∈Xn, denoted by On,p. This semigroup is nilpotent. In particular, the semigroup On,1 (i.e. p = 1) is already well studied, since it is the maximal nilpotent subsemigroup of the Catalan monoid. But the semigroup On,p is still not well [...]

The next meeting of the Algebra and Logic Seminar will be held on October 14, 2022 (Friday) at 1:00 pm (UTC+2) in Room 578 of IMI - BAS and online in Zoom. A talk on: Families of triple coverings of algebraic curves will be delivered by Hristo Iliev (American University in Bulgaria and IMI - BAS). Abstract. The talk is a continuation of my previous talk "Examples of non-reduced components of the Hilbert scheme of smooth projective curves using ruled surfaces" that I gave on August 19, 2022. In the present talk we consider curves that are triple covers of smooth projective curves of genus γ ≥ 0. We obtain families of curves on smooth surface scrolls which, under suitable numerical assumptions, yield components of [...]

The next meeting of the Algebra and Logic Seminar will be held on September 23, 2022 (Friday) at 1:00 pm (UTC+2) in Room 578 of IMI - BAS. A talk on: Geometry and logic in quantum computations will be delivered by Nikolay M. Nikolov (INRNE - BAS). Abstract. In 1936, Garrett Birkhoff and John Von Neumann published one of the most general axiomatic foundations of Quantum Theory, which has become known to this day as "Quantum Logic" (Annals of Mathematics, vol. 37 (1936) 823-843). In this work, they start from an ortho-modular lattice that serves as a model of the partially ordered set of all quantum events. They also found a connection with Projective Geometry. The main case of geometries is on complex numbers, but [...]

An online session of the Algebra and Logic Seminar will be held on September 16, 2022 (Friday) at 2:00 pm (UTC+3). A talk on: Almost Prime Ideal and Almost Prime Radical will be delivered by Alaa Abouhalaka (Çukurova University, Adana, Turkey). Abstract. 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).   Join Zoom meeting: https://us02web.zoom.us/j/85137375021?pwd=RE5QczdFTE1xL1R6MnI2b1lkcGczQT09 Topic: Онлайн семинар на секция "Алгебра и логика" Time: Sep 16, [...]

An online session of the Algebra and Logic Seminar will be held on September 9, 2022 (Friday) at 1:00 pm (UTC+3). A talk on: Timing delays in cyber-physical systems will be delivered by Naijun Zhan (Institute of Software Chinese Academy of Sciences ISCAS, China). Abstract. 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 [...]

An online session of the Algebra and Logic Seminar will be held on August 19, 2022 (Friday) at 1:00 pm (UTC+3). A talk on: Examples of non-reduced components of the Hilbert Scheme of smooth projective curves using ruled surfaces will be delivered by Hristo Iliev (American University in Bulgaria and IMI-BAS, Bulgaria). Abstract. 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 [...]

An online session of the Algebra and Logic Seminar will be held on July 29, 2022 (Friday) at 1:00 pm (UTC+3). A talk on: Modal Descriptive Complexity will be delivered by Petar Iliev (IPS-BAS and IMI-BAS, Bulgaria). Abstract.  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 [...]

An online session of the Algebra and Logic Seminar will be held on July 1, 2022 (Friday) at 1:00 pm (UTC+3). A talk on: On the parity of the coefficients of minimal polynomial of Kloosterman sums over Fp will be delivered by Lyubomir Borisov. Abstract. 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. [...]

An online session of the Algebra and Logic Seminar will be held on June 24, 2022 (Friday) at 1:00 pm (UTC+3). A talk on: Dependent-Type Theory of Situated Information with Context Assessments will be delivered by Roussanka Loukanova. Abstract. 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 [...]

An online session of the Algebra and Logic Seminar will be held on June 10, 2022 (Friday) at 4:00 pm (UTC+3). A talk on: Computing Eigenvectors of Symmetric Tridiagonals with the Correct Number of Sign Changes will be delivered by Plamen Koev (San José State University, USA). Abstract. 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: [...]