The next meeting of the Algebra and Logic Seminar will take place on June 19, 2026 (Friday) at 1:00 pm (UTC+3) in Room 578 and online via Zoom. A talk on: Varieties of left-commutative algebras will be delivered by Bekzat Zhakhayev (SDU University and Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan). (joint work with V. Drensky and V. Dotsenko) Abstract. An algebra A = (A, ・) is called a left-commutative algebra if it satisfies the identity a ・ (b ・ c) − b ・ (a ・ c) = 0 for all elements a, b, c ∈ A. We consider two subvarieties of the variety of left-commutative algebras, namely the varieties of Novikov algebras and bicommutative algebras. In 1976 Bokut formulated the following question: to describe, in terms of identities, varieties [...]

The next meeting of the Algebra and Logic Seminar will take place on April 24, 2026 (Friday) at 1:00 pm (UTC+3) in Room 578 and online via Zoom. A talk on: Sets preserved by a large subgroup of the special linear group will be delivered by Kaloyan Slavov (Medical University, Sofia). Abstract. The classical Kakeya problem in Euclidean space asks how “small” a set can be if it contains a unit line segment in every direction. More generally, packing sets contain all images of a given set under a collection of transformations. Finite field analogues offer a combinatorial and algebraic perspective and motivate our work. We study sets E in the affine plane over a finite field that are invariant under a large subgroup R [...]

The next meeting of the Algebra and Logic Seminar will take place on April 3, 2026 (Friday) at 1:00 pm (UTC+3) in online format via Zoom. A talk on: On Pairs of Non-commuting Hermitian Operators on the Unitary Plane which are Permutable Measurements will be delivered by Valentin Iliev (IMI-BAS). Abstract. In this presentation we study observables with spectre {-1,1} on quantum systems with the unitary plane as a space of states. Examples of such quantum systems are spin-1/2 particles. We find necessary and sufficient conditions for two non-commuting observables to be permutable measurements, that is, the probability of obtaining a particular pair of results does not depend on the order of taking these measurements. Several examples are presented. Link to the zoom meeting: https://us02web.zoom.us/j/88300991142?pwd=wGYl7VaD9RZKEm99sKzHMzl3bYCv3J.1 [...]

The next meeting of the Algebra and Logic Seminar will take place in hybrid form on December 5, 2025 (Friday) at 1:00 pm (UTC+3) in Room 578 of IMI-BAS and online via Zoom. A talk on: Classical Results in ITL with the Neighbourhood Modalities and Their Short Proofs Using Separation will be delivered by Dimitar Guelev (IMI-BAS). Link to the zoom meeting: Https://us02web.zoom.us/j/85137375021?pwd=RE5QczdFTE1xL1R6MnI2b1lkcGczQT09 Everybody is invited. Algebra and Logic Department, IMI - BAS http://www.math.bas.bg/algebra/seminarAiL/ ============================== =====================

The next meeting of the Algebra and Logic Seminar will take place in hybrid form on October 3, 2025 (Friday) at 1:00 pm (UTC+3) in Room 578 of IMI-BAS and online via Zoom. A talk on: Decomposition of Tschirnhausen Modules for Coverings on Decomposable P1-Bundles will be delivered by Hristo Iliev (American University in Bulgaria and IMI-BAS). Abstract Link to the zoom meeting: Https://us02web.zoom.us/j/85137375021?pwd=RE5QczdFTE1xL1R6MnI2b1lkcGczQT09 Everybody is invited. 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 July 25, 2025 (Friday) at 1:00 pm (UTC+3) in Room 578 of IMI-BAS. A talk on: Distinctness of the “lifted” Kloosterman sums over the prime field Fp will be delivered by Lyubomir Borissov (IMI - BAS). Abstract Everybody is invited. 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 June 6, 2025 (Friday) at 12:30 pm (UTC+3) in Room 578 of IMI-BAS. A talk on: Holographic probe branes and artificial neural networks will be delivered by Veselin Filev (IMI - BAS). Abstract: In holography, flavour probe branes are used to introduce fundamental matter to the AdS/CFT correspondence. At a technical level, the probes are described by extremizing the DBI action and solving the Lagrange–Euler equations of motion. I will report on applications of artificial neural networks that allow direct minimization of the regularized DBI action (interpreted as a free energy) without the need to derive and solve the equations of motion. I will consider, as examples, magnetic catalysis of chiral symmetry [...]

The next meeting of the Algebra and Logic Seminar will be held on May 16, 2025 (Friday) at 1:00 pm (UTC+2) in Room 503 of IMI-BAS. A talk on: Grätzer-Schmidt Theorem in arithmetical transfinite recursion will be delivered by Soowhan Yoon (American University in Bulgaria). Abstract: We assess the reverse mathematical strength of the Grätzer-Schmidt theorem (GS) as a principle in second order arithmetic. The theorem GS was studied in an article by Katie Brodhead, Mushfeq Khan, Bjørn Kjos-Hanssen, William A. Lampe, Paul Kim Long V. Nguyen, and Richard A. Shore, where they establish the provability of GS in Π11 Comprehension (Π11-CA0) and its restrictive variant GSD in arithmetical comprehension (ACA0). It will be shown that the arithmetical transfinite recursion (ATR0) is sufficient to prove GS. [...]