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 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 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 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 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, [...]

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 [...]

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 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 21, 2022 (Friday) at 1:00 pm (UTC+2) online in Zoom. A talk on: Gabbay Separation for the Duration Calculus will be delivered by Dimitar Guelev (IMI - BAS). Abstract.  Gabbay's separation theorem about linear temporal logic (LTL) with past has proved to be one of the most useful theoretical results in temporal logic. Is expressive power ultimately affected, if past constructs are not allowed in the scope of future ones, or vice versa? Separation implies that it does not, and also provides a technically convenient normal form for temporal conditions. Interval Temporal Logic (ITL) and the Duration Calculus (DC) are interval-based logics. Unlike LTL, they are based on modalities which [...]

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The next meeting of the Algebra and Logic Seminar will be held on December 2, 2022 (Friday) at 1:00 pm (UTC+2) online in Zoom. A talk on: Derivations of upper triangular matrix rings vs Derivations of upper triangular matrix semirings will be delivered by Dimitrinka Vladeva (IMI - BAS). Abstract. The motivation for this talk is the problem how to represent a derivation of a matrix ring and of an additively idempotent matrix semiring as a sum of well-known derivations. The results of two of my articles, published in 2022, will be compared and we will draw conclusions about the advantages and disadvantages of these results. We begin by considering the nature of derivations of triangular matrices over an additively idempotent semiring R generated [...]

The next meeting of the Algebra and Logic Seminar will be held on December 9, 2022 (Friday) online in Zoom where two talks will be delivered. From 1:00 pm to 2:00 pm (UTC+2) a talk on: AdS/CFT Correspondence, Metropolis-Hastings algorithm and Generative Adversarial Networks will be delivered by Veselin Filev (IMI - BAS). Abstract. I will report on a recent publication on the construction of a backreacted D0/D4 background. I will discuss the relevance of this study in the AdS/CFT correspondence and the simulation of the Berkooz-Douglas matrix model. In the second part of the talk, I will review the Metropolis-Hastings algorithm and report on possible applications of the Generative Adversarial Networks (GANs) in the simulation of computationally expensive matrix models. From 2:00 pm [...]

The next meeting of the Algebra and Logic Seminar will be held on January 13, 2023 (Friday) online in Zoom. A talk on: Artificial Intelligence - Definition, Implementation and Consequences will be delivered by Dimitar Dobrev (IMI - BAS).   The seminar will be held online. Join the Zoom link: https://us02web.zoom.us/j/85137375021?pwd=RE5QczdFTE1xL1R6MnI2b1lkcGczQT09 Topic: Онлайн семинар на секция "Алгебра и логика" Time: Jan 13, 2023 01:00 PM Sofia Meeting ID: 851 3737 5021 Passcode: 035647 Algebra and Logic Department, IMI - BAS http://www.math.bas.bg/algebra/seminarAiL/ ============================== =====================

The next meeting of the Algebra and Logic Seminar will be held on February 10, 2023 (Friday) online in Zoom. A talk on: A New Approach to the Characteristic Polynomial of a Random Unitary Matrix will be delivered by Yacine Barhoumi-Andréani (Ruhr-Universität Bochum, Germany). Abstract. The characteristic polynomial of a random (Haar-distributed) unitary matrix is considered as an interesting toy model for the probabilistic study of the Riemann Zeta function. We will recall the history of the topic starting with the Montgommery-Dyson correspondance, the Keating-Snaith moments conjecture and some recent developments on other functionals. We will then give a conceptual comparison of some of the techniques used in the field and a zoo of results one can achieve, with a particular focus on a [...]

The next meeting of the Algebra and Logic Seminar will be held on February 17, 2023 (Friday) online in Zoom. A talk on: Invariant theory for reductive subgroups of reductive groups will be delivered by Valdemar Tsanov (IMI-BAS). Abstract.Let H ⸦ G be an embedding of connected complex reductive linear algebraic groups. A classical question with several important interpretations is: which irreducible G-modules contain nonzero H-invariant vectors? An approach based on the Geometric Invariant Theory of Hilbert-Mumford was developed in works of Heckman, Berenstein-Sjamaar, Belkale-Kumar and Ressayre, culminating in a description of the generalized Littlewood-Richadson cone - the convex hull of set of the highest weights of the G-modules containing H-invariants. The discrepancy between the convex hull and the actual set of weights presents [...]

The next meeting of the Algebra and Logic Seminar will be held on February 24, 2023 (Friday) online in Zoom. A talk on: Real Hamiltonian forms of affine Toda field theories: spectral aspects will be delivered by Vladimir Gerdjikov (joint work with G. G. Grahovski and A. A. Stefanov). Abstract. The talk is devoted to real Hamiltonian forms of 2-dimensional Toda field theories related to exceptional simple Lie algebras, and to the spectral theory of the associated Lax operators. Real Hamiltonian forms are a special type of reductions of Hamiltonian systems, similar to real forms of semisimple Lie algebras. The real Hamiltonian forms of affine Toda field theories related to exceptional complex untwisted affine Kac - Moody algebras are studied. Along with the associated Lax [...]