An online session of the Algebra and Logic Seminar will be held on February 19, 2021 (Friday) at 1:00 p.m. A talk on Identities in Prime Rings will be delivered by Jose Brox (Centre for Mathematics of the University of Coimbra, Portugal). Abstract. Given a ring, a generalized polynomial identity (GPI) is a polynomial identity in which the coefficients can be taken from the ring. Prime rings are a class of rings very well suited to manage problems related to identities, as for example those coming from Herstein's theory, which is the study of nonassociative objects and structures arising from associative rings. After a motivating introduction to prime rings, with some examples from Herstein's theory, I will show the usefulness of Martindale's lemma, the [...]

An online session of the Algebra and Logic Seminar will be held on February 26, 2021 (Friday) at 1:00 p.m. A talk on Enumeration Reducibility: 60 years of investigation will be delivered by Hristo Ganchev (Faculty of Mathematics and Informatics of the Sofia University). Abstract. We will make an overview of the main results and problems in Еnumeration reducibility – one of the two main reducibilities used to compare the complexity of the information content in sets of natural numbers.   The seminar will be held via Zoom and everyone can join via the link: https://us02web.zoom.us/j/85137375021?pwd=RE5QczdFTE1xL1R6MnI2b1lkcGczQT09 Topic: Онлайн семинар на секция "Алгебра и логика" Time: Feb 26, 2021 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 5, 2021 (Friday) at 4:00 p.m. A talk on Finite presentability for metabelian groups, Lie algebras and restricted Lie algebras will be delivered by Dessislava Kochloukova, University of Campinas, Brazil. Abstract. In the first part of the talk we revisе the already known classifications of finite presentability (in terms of generators and relations) for metabelian groups and metabelian Lie algebras. The case of groups was solved by Robert Bieri and Ralph Strebel in 1980s and that of Lie algebras was done by Roger Bryant and John Groves in late 1990s. In the last part of the talk we discuss new results about the classification of finitely presented metabelian restricted Lie algebras [...]

An online session of the Algebra and Logic Seminar will be held on March 19, 2021 (Friday) at 4:00 p.m. A talk on Some applications of transfinite numbers to algebra and some applications of number theory to transfinite numbers will be delivered by Andreas Weiermann (Ghent University, Belgium). Abstract.  In the first part we will survey the role of transfinite numbers in the study of Hilbert's basis theorem and its extension by MacLagan. To this end we associate ordinals to some natural well partial orderings related Cartesian products of the set of natural numbers and we apply this apparatus to monomial ideals in F[X_1,...,X_n] where F is a field. In the second part we use the machinery of Tauberian theorems to prove some structural results [...]

An online session of the Algebra and Logic Seminar will be held on March 26, 2021 (Friday) at 1:00 p.m. A talk on Some axioms about rationality in infinite concurrent multiplayer games with ordered objectives and temporary coalitions in QCTL* will be delivered by Dimitar Guelev (IMI - BAS). Abstract. Temporal winning conditions appear in both terminating and infinite games. Reachability (guarantee) winning conditions appear in terminating games. Safety conditions and conditions higher up in the (Manna & Pnueli, 1989) hierarchy appear in non-terminating games. In a multiplayer game, the latter classes of winning conditions are natural to drive players into forming permanent coalitions as the longevity of a coalition needs to match the duration of its agenda, which may take entire infinite plays [...]

An online session of the Algebra and Logic Seminar will be held on March 26, 2021 (Friday) at 1:00 p.m. A talk on Universal tensor categories and “algebraic functional analysis” will be delivered by Ivan Penkov (Jacobs University Bremen, Germany). Abstract. In this talk I will outline the construction of some tensor categories generated by two objects X, Y with a pairing X\otimes Y → 1 to the monoidal unit 1. These categories are categories of representations of certain infinite-dimensional Lie algebras, and they turn out to be universal in a sense which will be explained in the talk. The interpretation of Y as a dual space to X allows an analogy with functional analysis. Joint work with A. Chirvasitu, based on earlier joint work [...]

On April 16, 2021 (Friday) at 4:00 p.m. Assoc. Prof. Veselin Filev (IMI - BAS) will deliver his inaugural lecture on The Holographic Principle – Motivation and Applications Abstract. I will talk about the arguments that lead to the formulation of the holographic principle and its realization in the framework of superstring theory via the AdS/CFT correspondence. I will focus on the applications of the holographic principle for the description of confinement, chiral symmetry breaking and novel phases of strongly interacting matter.   The lecture will be held via Zoom and everyone can join at: https://us02web.zoom.us/j/85137375021?pwd=RE5QczdFTE1xL1R6MnI2b1lkcGczQT09 Time: Apr 16, 2021 04:00 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 April 23, 2021 (Friday) at 4:00 p.m. (+3 UTC) A talk on On Krull dimension of Noetherian super-rings will be delivered by Alexandr Zubkov (United Arab Emirates University, Al Ain, UAE and Sobolev Institute of Mathematics (Omsk branch), Omsk, Russia). Abstract. The notion of Krull dimension plays crucial role in the algebraic geometry and in the theory of commutative rings. It seems quite natural to define such a notion for (supercommutative) super-rings in order to develop the algebraic supergeometry in more or less systematic way, similar to the classical case. This talk is partially based on the recent joint work with A. Masuoka (published in JPAA) and new results (yet unpublished).   The [...]

On April 29, 2021 (Thursday) at 3:00 p.m. (UTC +3) Assoc. Prof. Peter Danchev (IMI - BAS) will deliver his inaugural lecture on Commutative Group Rings and Abelian Groups Abstract. Some specific questions from the theory of commutative group rings and Abelian groups are being considered as complete solutions to some of them are given, which definitely generalize certain classical results in these directions.   The lecture will be held via Zoom and everyone can join at: https://us02web.zoom.us/j/85137375021?pwd=RE5QczdFTE1xL1R6MnI2b1lkcGczQT09 Time: Apr 29, 2021 03:00 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 May 7, 2021 (Friday) at 1:00 p.m. (+3 UTC) A talk on On the Degree of Dependence of Two Events will be delivered by Valentin Iliev. Abstract. We define degree of dependence of two events A and B in a probability space by using Boltzmann-Shannon entropy function of an appropriate distribution produced by these events and depending on one parameter varying within a closed interval I. The important particular case of discrete uniform probability space motivates this definition in the following way. The entropy function has a global maximum exactly when the events A and B are independent. It has a minimum at the left endpoint of I exactly when A is [...]

An online session of the Algebra and Logic Seminar will be held on May 14, 2021 (Friday) at 1:00 p.m. (+3 UTC) A talk on Non-finitely based and limit varieties of algebraic systems will be delivered by Vesselin Drensky. Abstract. A variety of algebraic systems is non-finitely (or infinitely) based if it does not have a finite basis of identities. It is just-non-finitely based (or limit) if it is non-finitely based but all its proper subvarieties are finitely based. By the Zorn lemma every variety without a finite basis of identities contains a just-non-finitely based subvariety. We survey results on non-finitely based varieties of groups, semigroups and on associative, Lie and nonassociative rings and algebras. We also present examples of just-non-finitely based varieties of nonassociative [...]

An online session of the Algebra and Logic Seminar will be held on May 21, 2021 (Friday) at 4:00 p.m. (+3 UTC) A talk on Group gradings on incidence algebras will be delivered by Ednei Aparecido Santulo Jr. (Universidade Estadual de Maringá, Paraná, Brazil). Abstract. This is a joint work with Felipe Y. Yasumura and Jonathan P. Souza. The main goal of this talk is presenting the classification of group gradings on incidence algebras as obtained in [2]. To do so, we start by defining incidence algebras and emphasizing their resemblances and differences relative to the algebra of upper triangular matrices. We recall the classification of group gradings on the algebra of upper triangular matrices with entries in a field obtained by Di Vincenzo, Koshlukov [...]

An online session of the Algebra and Logic Seminar will be held on May 28, 2021 (Friday) at 1:00 p.m. (+3 UTC) A talk on Ranks of Monoids of Endomorphisms, Partial Automorphisms and Injective Partial Endomorphisms of a Finite Undirected Path will be delivered by Ilinka Dimitrova (South-West University “Neofit Rilski”, Blagoevgrad). This is a joint work with Vitor H. Fernandes (Universidade Nova de Lisboa, Caparica, Portugal), Jörg Koppitz (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences), Teresa M. Quinteiro (Universidade Nova de Lisboa, Caparica, Portugal). 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: May 28, 2021 01:00 PM Sofia Meeting ID: 851 3737 5021 Passcode: 035647   [...]

An online session of the Algebra and Logic Seminar will be held on June 4, 2021 (Friday) at 1:00 p.m. (+3 UTC) A talk on Schur’s exponent conjecture will be delivered by Michael Vaughan-Lee (Oxford University Mathematical Institute, United Kingdom).   Abstract. If G is a finite group and we write G = F/R where F is a free group, then the Schur multiplier M(G) is (R \cap F’)/[R, F]. There is a long-standing conjecture attributed to I. Schur that the exponent of M(G) divides the exponent of G. It is easy to show that this is true for groups G of exponent 2 or exponent 3, but it has been known since 1974 that the conjecture fails for exponent 4. However the truth or [...]

An online session of the Algebra and Logic Seminar will be held on June 11, 2021 (Friday) at 1:00 p.m. (UTC +3) A talk on Distinctness of the “lifted” Kloosterman sums over the prime field F_p will be delivered by Lyubomir Borissov. 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: June 04, 2021 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 June 18, 2021 (Friday) at 1:00 p.m. (UTC +3) A talk on Primary decompositions of unital locally matrix algebras and Steinitz numbers will be delivered by Bogdana Oliynik (National University of Kyiv-Mohyla Academy, Kyiv, Ukraine). Abstract. Let F be a ground field. An F-algebra A with unit 1 is said to be a locally matrix algebra if an arbitrary finite collection of elements a1, . . . , as from A lies in a subalgebra B with 1 of the algebra A, and B is isomorphic to a matrix algebra Mn(F), n ≥. We assign a Steinitz number n(A) to an arbitrary unital locally matrix algebra A. In this talk, we [...]

An online session of the Algebra and Logic Seminar will be held on June 25, 2021 (Friday) at 11:00 a.m. (UTC +3). A talk on Framing in secret sharing  will be delivered by Arkadii Slinko (The University of Auckland, New Zealand). Abstract. Secret sharing, a well-known cryptographic technique, introduced 40 years ago as a private and reliable variant of classical storage, has now become a major cryptographic primitive with numerous real-world applications. In this paper we consider the digital forensics aspects of secret sharing. We investigate the problem of framing which occurs when a coalition of participants is able to calculate the share of a participant who does not belong to it. In the extreme case one authorized coalition can calculate shares of another [...]

An online session of the Algebra and Logic Seminar will be held on July 2, 2021 (Friday) at 1:00 p.m. (UTC +3). A talk on Noncommutative Poisson structures, Hochschild type complexes and Gröbner bases theory will be delivered by Natalia Iyudu (Lancaster University, UK). Abstract: I will discuss Calabi-Yau type conditions, such as pre-Calabi-Yau and exact Calabi-Yau. We show that pre-Calabi-Yau structures give rise to double Pois son brackets of Van den Bergh. The homological formulation of pre-Calabi-Yau structure can be dealt with using Gröbner bases theory to prove purity in case of free graph path algebras. This technique is common for our study of such exact Calabi-Yau algebras as 3-Sklyanin. Here we are able, for example, to improve the statement in Artin-Schelter classical [...]

An online session of the Algebra and Logic Seminar will be held on July 9,  2021 (Friday) at 1:00 p.m. (UTC +3). A talk on The mysterious Kronecker coefficients of the Symmetric group will be delivered by Greta Panova (University of Southern California, USA). Abstract. Algebraic Combinatorics is a field of mathematics which studies discrete objects often originating in Representation Theory, Algebra, Algebraic Geometry, Number Theory via combinatorial methods. One of its oldest problems concerns the Kronecker coefficients of the Symmetric Group. They are originally defined by Murnaghan more than 80 years ago as the multiplicities of the irreducible modules in the factorization of the tensor product of two other irreducible modules. They actually generalize the Littlewood-Richardson coefficients in the analogous problem for the [...]

An online session of the Algebra and Logic Seminar will be held on July 16, 2021 (Friday) at 1:00 p.m. (UTC +3). A talk on Proof Complexity of Resolution over linear inequalities will be delivered by Stefan Dantchev (Durham University, United Kingdom). Abstract. I will start by giving a brief and non-comprehensive introduction to the general research area, Propositional Proof Complexity. I will then focus on a specific proof system that operates on linear inequalities with integral coefficients, called Stabbing Planes (SP). Next, a general method for proving depth lower bounds in SP will be introduced, which allows us to prove logarithmic depth lower bounds for several well-studied propositional contradictions, such as the Pigeon-Hole Principle and the Ordering Principle. Finally, possible extensions and generalisations [...]

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' [...]