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 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 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 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 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 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 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 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 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 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   [...]