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. [...]

The next meeting of the Algebra and Logic Seminar will be held on April 25, 2025 (Friday) at 1:00 pm (UTC+2) in Room 578 of IMI-BAS. A talk on: Hilbert scheme of smooth projective curves and some easy examples will be delivered by Changho Keem (Seoul National University, South Korea). Abstract: Hilbert scheme is a parameter space for a family of projective algebraic varieties sharing a given fixed Hilbert polynomial.  In this talk, we will discuss the following topics concerning the Hilbert scheme of smooth projective algebraic curves. 1. Irreducibility problem of the restricted Hilbert scheme of curves. 2. Some easy examples of reducible Hilbert schemes inside or outside the Brill-Noether range. 3. The existence of more than expected dimensional components whose image under the moduli [...]