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 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 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 [...]

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 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 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 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 [...]

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 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 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 [...]