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 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 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/ ===============================