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 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 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 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 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 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 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 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 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 [...]