An online session of the Algebra and Logic Seminar will be held on September 17, 2021 (Friday) at 11:00 a.m. (UTC +3). A talk on Dessins d’enfants and moduli spaces of curves will be delivered by George Shabat (Russian State University for the Humanities and Independent University of Moscow, Russia). Abstract The seminar will be held via Zoom and everyone can join at: https://us02web.zoom.us/j/85137375021?pwd=RE5QczdFTE1xL1R6MnI2b1lkcGczQT09  Topic: Онлайн семинар на секция "Алгебра и логика" Time: Sep 17, 2021 11:00 AM Sofia Meeting ID: 851 3737 5021 Passcode: 035647 Algebra and Logic Department, IMI-BAS http://www.math.bas.bg/algebra/seminarAiL/ ============================== =====================

An online session of the Algebra and Logic Seminar will be held on October 22, 2021 (Friday) at 2:00 p.m. (UTC +3). A talk on On Some Special Decompositions of Matrices over Fields and Finite Commutative Rings will be delivered by Peter Danchev. Abstract. In order to find a suitable expression of an arbitrary square matrix over an arbitrary field, we prove that every square matrix over an infinite field is always representable as a sum of a diagonalizable matrix and a square-zero nilpotent matrix. In addition, each 2 x 2 matrix over any field admits such a representation. We also show that, for all natural numbers n > 2, every n x n matrix over a finite field having no less than n [...]

An online session of the Algebra and Logic Seminar will be held on October 29, 2021 (Friday) at 5:00 p.m. (UTC +3). A talk on Tropical Geometry and the Commutative Algebra of Semirings will be delivered by Kalina Mincheva (Tulane University, New Orleans, USA). Abstract. Tropical geometry provides a new set of purely combinatorial tools, which has been used to approach classical problems. In tropical geometry most algebraic computations are done on the classical side - using the algebra of the original variety. The theory developed so far has explored the geometric aspect of tropical varieties as opposed to the underlying (semiring) algebra and there are still many commutative algebra tools and notions without a tropical analogue. In the recent years, there has been [...]

An online session of the Algebra and Logic Seminar will be held on November 5, 2021 (Friday) at 1:00 p.m. (UTC +2). A talk on Permutation groups and permutation patterns will be delivered by Erkko Lehtonen (Universidade Nova de Lisboa, Portugal). Abstract.  We approach permutations from two different points of view: the algebraic one of permutation groups and the combinatorial one of permutation patterns. While these two well-established notions do not seem to have much in common, there is a perhaps surprising connection that will be explained in this talk. Namely, the class of permutations avoiding the complement of a permutation group is comprised of levels that are permutation groups. With the help of invariant relations, we describe the permutation groups that arise in [...]

An online session of the Algebra and Logic Seminar will be held on November 19, 2021 (Friday) at 1:00 p.m. (UTC +2). A talk on Identities of Vector Spaces and Nonassociative Linear Algebras will be delivered by Alexey V. Kislitsin (Altai State Pedagogical University, Barnaul, Russia). This is a joint talk with Ismail M. Isaev (Altai State Pedagogical University, Barnaul, Russia). The talk will be delivered in Russian, the slides will be in English. Abstract. In this talk, we study the concept of the identity of the L-space as a weak identity of the pair (A, E), where A is the associative F-algebra generated by the vector space E over the field F. We study the properties of the L-spaces and their identities. Corollaries [...]

An online session of the Algebra and Logic Seminar will be held on November 26, 2021 (Friday) at 1:00 p.m. (UTC +2). A talk on On a method of proving the non-existence of modal formulae satisfying certain syntactic properties and defining a given class of frames will be delivered by Petar Iliev (Institute of Philosophy and Sociology and Institute of Mathematics and Informatics, Bulgarian Academy of Sciences). Abstract.  We elaborate on semantically labeled syntax trees, which provide a method of proving the non-existence of modal formulae satisfying certain syntactic properties and defining a given class of either models or frames, and use them to show that there are classes of Kripke frames that are definable by both non-Sahlqvist and Sahlqvist formulae but the latter [...]

An online session of the Algebra and Logic Seminar will be held on December 3, 2021 (Friday) at which two talks will be delivered. At 1:00 pm (UTC+2) a talk on A Separation Theorem for Discrete Time Interval Temporal Logic will be delivered by Dimitar Guelev *(joint work with Ben Moszkowski). The talk will be delivered in Bulgarian with presentation in English. Abstract. Gabbay's separation theorem about linear temporal logic with past is admittedly one of the most useful theoretical results in temporal logic. In this talk, we establish an analogous statement about Moszkowski’s discrete time propositional Interval Temporal Logic (ITL) with two sets of expanding modalities, namely the unary neighbourhood modalities and the binary weak inverses of ITL's chop operator. (The two pairs of [...]

An online session of the Algebra and Logic Seminar will be held on January 7, 2022 (Friday) at 1:00 pm (UTC+2). A talk on A valuation theorem for Noetherian rings will be delivered by Antoni Rangachev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences). Abstract. A classical result due to Krull says that a normal domain R is equal to the intersection of the valuation rings in its field of fractions that contain R. If in addition R is Noetherian, then one can restrict the intersection to the discrete valuation rings that contain R. Now consider the following relative setting. Let A and B be integral domains. Suppose A is Noetherian and B is a finitely generated A-algebra that contains A. Denote by A' [...]

An online session of the Algebra and Logic Seminar will be held on January 21, 2022 (Friday) at 1:00 pm (UTC+2). A talk on On the distribution of αp modulo one for primes p=aq^2+1 with prime q will be delivered by Tatyana Todorova (FMI, Sofia University, Bulgaria). Abstract. It is a long-standing conjecture that there are infinitely many primes of the form n^2+1. Several approximations to this problem have been made. Baier and Zhao showed that for any ε > 0, there are infinitely many primes of the form p = aq^2 + 1, where a ≤ p^(5/9+ε). The best known result, due to Matomäki is that there are infinitely many primes of the form p = aq^2 + 1, where a ≤ p^(1/2+ε) and [...]

An online session of the Algebra and Logic Seminar will be held on January 28, 2022 (Friday) at 1:00 pm (UTC+2). A talk on: Bicommutative algebras from commutative point of view will be delivered by Vesselin Drensky (IMI - BAS). Abstract: The nonassociative algebra R is right-commutative if (ab)c = (ac)b for all a, b, c in R, R is left-commutative if a(bc) = b(ac) for all a, b, c in R. Bicommutative algebras are algebras which are both left- and right-commutative. One-sided commutative algebras appeared for the first time in a paper by Cayley in 1857. Their important subclass of Gelfand-Dorfman-Novikov algebras were studied by Gelfand and Dorfman for the needs of the Hamiltonian operator in finite-dimensional mechanics and by Balinskii and Novikov [...]

An online session of the Algebra and Logic Seminar will be held on February 11, 2022 (Friday) at 1:00 pm (UTC+2). A talk on: Modal definability of some classes of modal products will be delivered by Yana Rumenova (FMI - Sofia University). This is a joint work with Tinko Tinchev (FMI - Sofia University). Abstract The seminar will be held via Zoom and anyone can join at: https://us02web.zoom.us/j/85137375021?pwd=RE5QczdFTE1xL1R6MnI2b1lkcGczQT09 Topic: Онлайн семинар на секция "Алгебра и логика" Time: Feb 11, 2022 01:00 PM Sofia Meeting ID: 851 3737 5021 Passcode: 035647 Algebra and Logic Department, IMI-BAS http://www.math.bas.bg/algebra/seminarAiL/ ============================== =====================

An online session of the Algebra and Logic Seminar will be held on February 18, 2022 (Friday) at 4:00 pm (UTC+2). A talk on: The Bulgarian Solitaire and Other Games on Partitions will be delivered by Vesselin Drensky (IMI - BAS). Abstract. In 2020 the L.N. Gumilyov Eurasian National University (Nur-Sultan, Kazakhstan) decided to organize International Scientific Conference "Algebra and Logic" dedicated to the 60th anniversary of Professor Ualbai Umirbaev and the 75th anniversary of Professor Leonid Makar-Limanov. The meeting was cancelled because of the Covid-19 pandemic. The present talk is based on the talk I planned to give in Nur-Sultan. The (quite amusing) story presented in the talk is an example of how an elementary mathematical game can inspirit serious mathematical investigations in [...]

An online session of the Algebra and Logic Seminar will be held on February 25, 2022 (Friday) at 1:00 pm (UTC+2). A talk on: On the Degree of Dependence of Two Events as a Relative Invariant of the Dihedral Group of Order 8 will be delivered by Valentin Iliev (IMI - BAS). Abstract The seminar will be held via Zoom and anyone can join at: https://us02web.zoom.us/j/85137375021?pwd=RE5QczdFTE1xL1R6MnI2b1lkcGczQT09 Topic: Онлайн семинар на секция "Алгебра и логика" Time: Feb 25, 2022 01:00 PM Sofia Meeting ID: 851 3737 5021 Passcode: 035647 Algebra and Logic Department, IMI-BAS http://www.math.bas.bg/algebra/seminarAiL/ ============================== =====================

An online session of the Algebra and Logic Seminar will be held on March 11, 2022 (Friday) at 2:00 pm (UTC+2). A talk on: Multi-summation in difference rings and applications will be delivered by Carsten Schneider (Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria). Abstract. Symbolic summation in difference fields started with Karr's summation algorithm (1981) which can be considered as the discrete version of Risch's indefinite integration algorithm in differential fields. In the last 20 years this approach has been generalized and enhanced to a constructive summation theory of difference rings. In general, one can represent algorithmically any expression in terms of indefinite nested sums defined over hypergeometric products in such rings. As a crucial by-product one obtains optimal representations where the [...]

An online session of the Algebra and Logic Seminar will be held on March 18, 2022 (Friday) at 4:00 pm (UTC+2). A talk on: Absorbing ideal structures of commutative rings will be delivered by Ece Yetkin Celikel (Hasan Kalyoncu University, Turkey). Abstract. Let R be a commutative ring with nonzero identity. As generalizations of prime ideals, the absorbing ideals were first defined and studied by A. Badawi in 2007. A proper ideal I of R is said to be 2-absorbing if whenever a, b, c ∈ R with abc ∈ I, then either ab ∈ I or ac ∈ I or bc ∈ I. After this date, many researches have been done to introduce various extensions of this concept. In this talk, we present [...]

An online session of the Algebra and Logic Seminar will be held on March 25, 2022 (Friday) at 1:00 pm (UTC+2). A talk on: An Application of Separation in Discrete Time Interval Temporal Logic to Branching Time will be delivered by Dimitar Guelev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences). Abstract. In this talk we make an application of our separation theorem for discrete time Interval Temporal Logic (ITL) to the study of Interval-based Computation Tree Logic (ICTL*). We prove that the expressibility of the expanding modalities and, most importantly, propositional quantification, carry over from linear time ITL to the branching time system of ICTL*. The relevance of this follows from the fact that point-based propositionally quantified CTL* (QCTL*) is the established intermediate [...]

An online session of the Algebra and Logic Seminar will be held on April 1, 2022 (Friday) at 1:00 pm (UTC+3). A talk on: Automorphisms of simple quotients of the Poisson and universal enveloping algebras of sl_2 will be delivered by Altyngul Naurazbekova (L. N. Gumilyov Eurasian National University, Nur-Sultan, Kazakhstan). Abstract. Let P(sl_2(K)) be the Poisson enveloping algebra of the Lie algebra sl_2(K) over an algebraically closed field K of characteristic zero. U. Umirbaev, V. Zhelyabin proved that the quotient algebras P(sl_2(K))/(C_P - λ), where C_P is the standard Casimir element of sl_2(K) in P(sl_2(K)) and 0 ≠ λ ∈K, are simple. Using a result by L. Makar-Limanov on groups of automorphisms of a class of surfaces, we describe generators of the automorphism group [...]

An online session of the Algebra and Logic Seminar will be held on April 15, 2022 (Friday) at 1:00 pm (UTC+3). A talk on: Quantisation of free associative dynamical systems. Bi-quantum structure of the stationary KdV hierarchy. Non-deformation quantisation of the Volterra hierarchy will be delivered by Alexander V. Mikhailov (University of Leeds, UK). Abstract. Traditional quantisation theories start with classical Hamiltonian systems with variables taking values in commutative algebras and then study their non-commutative deformations, such that the commutators of observables tend to the corresponding Poisson brackets as the (Planck) constant of deformation goes to zero. I am proposing to depart from dynamical systems defined on a free associative algebra A. In this approach the quantisation problem is reduced to the problem of finding [...]

An online session of the Algebra and Logic Seminar will be held on April 29, 2022 (Friday) at 4:00 pm (UTC+3). A talk on: Images of multilinear polynomials on upper triangular matrices will be delivered by Thiago Castilho de Mello (Universidade Federal de São Paulo, Brazil). Abstract.  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 [...]

An online session of the Algebra and Logic Seminar will be held on May 13, 2022 (Friday) at 1:00 pm (UTC+3). A talk on: A counterexample to the modular isomorphism problem will be delivered by Diego García-Lucas (Universidad de Murcia, Spain). Abstract. 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 [...]

An online session of the Algebra and Logic Seminar will be held on May 20, 2022 (Friday) at 4:00 pm (UTC+3). A talk on: Bootstrap percolation: merging operations for polytopes will be delivered by Ivailo Hartarsky (Université Paris-Dauhpine, PSL, France, visiting scholar at Instituto de Matemática Pura e Aplicada, Rio de Janeiro, Brazil). Abstract. 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 [...]

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: [...]

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 [...]