The next meeting of the Algebra and Logic Seminar will be held on June 16, 2023 (Friday) at 1:00 pm (UTC+3) online in Zoom. A talk on: Polynomial identities in Novikov algebras will be delivered by Nurlan Ismailov (Astana IT University and Suleyman Demirel University, Kaskelen, Kazakhstan) (Joint work with V. Dotsenko and U. Umirbaev). Abstract.The talk is devoted to Novikov algebras satisfying nontrivial identities. We show that a Novikov algebra over a field of zero characteristic that satisfies a nontrivial identity satisfies some unexpected “universal” identities, in particular, right associator nilpotence, and right nilpotence of the commutator ideal. This, in particular, implies that a Novikov algebra over a field of zero characteristic satisfies a nontrivial identity if and only if it is Lie-solvable. We [...]

The next meeting of the Algebra and Logic Seminar will be held on June 9, 2023 (Friday) at 1:00 pm (UTC+3) online in Zoom. A talk on: Old and new aspects of the Poincaré-Birkhoff-Witt theorem will be delivered by Vladimir Dotsenko (Institute for Advanced Mathematical Research (IRMA), University of Strasbourg and CNRS, France). Abstract.The Poincaré-Birkhoff-Witt theorem on universal enveloping algebras of Lie algebras is a fundamental result in many areas of mathematics: from differential geometry and representation theory to homological algebra and deformation quantization. I shall give a short overview of that result and some of its proofs that emerged in about 120 years since Poincaré published a paper about it, and outline a new proof which perhaps captures its category-theoretic essence in the best [...]

The next meeting of the Algebra and Logic Seminar will be held on May 5, 2023 (Friday) at 1:00 pm (UTC+3) online in Zoom. Prof. Jörg Koppitz will deliver his inaugural lecture on: Algebraic Properties of Transformation Semigroups Abstract. Each semigroup is isomorphic to a semigroup of transformations on a suitable set (Cayley Theorem for semigroups). If we know generating sets of minimal size (rank) of a finitely generating semigroup then we have important information about the algebraic structure of the semigroup itself. For not finitely generated semigroups, we consider relative generating sets of minimal size modulo a given subset of the semigroup (relative rank). We determine the (relative) rank of several semigroups of transformations. These semigroups were already considered by other authors. By the study [...]

The next meeting of the Algebra and Logic Seminar will be held on April 7, 2023 (Friday) at 1:00 pm (UTC+3) online in Zoom. A talk on: Exact values of exponential Følner functions and the Coulhon and Saloff-Coste inequality will be delivered by Bogdan Stankov (Institut Camille Jordan, Université Claude Bernard Lyon 1, France). Abstract.For infinite groups, the Følner criterion states that a group is amenable if and only if the isoperimetric constant of its Cayley graph is 0. In that case, a more precise description of its isoperimetric profile is given by the Følner function. It depends on the choice of generating set, but different functions on the same group are asymptotically equivalent. Multiple results have been obtained on Følner functions, but only up [...]

The next meeting of the Algebra and Logic Seminar will be held on February 24, 2023 (Friday) online in Zoom. A talk on: Real Hamiltonian forms of affine Toda field theories: spectral aspects will be delivered by Vladimir Gerdjikov (joint work with G. G. Grahovski and A. A. Stefanov). Abstract. The talk is devoted to real Hamiltonian forms of 2-dimensional Toda field theories related to exceptional simple Lie algebras, and to the spectral theory of the associated Lax operators. Real Hamiltonian forms are a special type of reductions of Hamiltonian systems, similar to real forms of semisimple Lie algebras. The real Hamiltonian forms of affine Toda field theories related to exceptional complex untwisted affine Kac - Moody algebras are studied. Along with the associated Lax [...]

The next meeting of the Algebra and Logic Seminar will be held on February 17, 2023 (Friday) online in Zoom. A talk on: Invariant theory for reductive subgroups of reductive groups will be delivered by Valdemar Tsanov (IMI-BAS). Abstract.Let H ⸦ G be an embedding of connected complex reductive linear algebraic groups. A classical question with several important interpretations is: which irreducible G-modules contain nonzero H-invariant vectors? An approach based on the Geometric Invariant Theory of Hilbert-Mumford was developed in works of Heckman, Berenstein-Sjamaar, Belkale-Kumar and Ressayre, culminating in a description of the generalized Littlewood-Richadson cone - the convex hull of set of the highest weights of the G-modules containing H-invariants. The discrepancy between the convex hull and the actual set of weights presents [...]

The next meeting of the Algebra and Logic Seminar will be held on February 10, 2023 (Friday) online in Zoom. A talk on: A New Approach to the Characteristic Polynomial of a Random Unitary Matrix will be delivered by Yacine Barhoumi-Andréani (Ruhr-Universität Bochum, Germany). Abstract. The characteristic polynomial of a random (Haar-distributed) unitary matrix is considered as an interesting toy model for the probabilistic study of the Riemann Zeta function. We will recall the history of the topic starting with the Montgommery-Dyson correspondance, the Keating-Snaith moments conjecture and some recent developments on other functionals. We will then give a conceptual comparison of some of the techniques used in the field and a zoo of results one can achieve, with a particular focus on a [...]

The next meeting of the Algebra and Logic Seminar will be held on January 13, 2023 (Friday) online in Zoom. A talk on: Artificial Intelligence - Definition, Implementation and Consequences will be delivered by Dimitar Dobrev (IMI - BAS).   The seminar will be held online. Join the Zoom link: https://us02web.zoom.us/j/85137375021?pwd=RE5QczdFTE1xL1R6MnI2b1lkcGczQT09 Topic: Онлайн семинар на секция "Алгебра и логика" Time: Jan 13, 2023 01:00 PM Sofia Meeting ID: 851 3737 5021 Passcode: 035647 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 December 9, 2022 (Friday) online in Zoom where two talks will be delivered. From 1:00 pm to 2:00 pm (UTC+2) a talk on: AdS/CFT Correspondence, Metropolis-Hastings algorithm and Generative Adversarial Networks will be delivered by Veselin Filev (IMI - BAS). Abstract. I will report on a recent publication on the construction of a backreacted D0/D4 background. I will discuss the relevance of this study in the AdS/CFT correspondence and the simulation of the Berkooz-Douglas matrix model. In the second part of the talk, I will review the Metropolis-Hastings algorithm and report on possible applications of the Generative Adversarial Networks (GANs) in the simulation of computationally expensive matrix models. From 2:00 pm [...]

The next meeting of the Algebra and Logic Seminar will be held on December 2, 2022 (Friday) at 1:00 pm (UTC+2) online in Zoom. A talk on: Derivations of upper triangular matrix rings vs Derivations of upper triangular matrix semirings will be delivered by Dimitrinka Vladeva (IMI - BAS). Abstract. The motivation for this talk is the problem how to represent a derivation of a matrix ring and of an additively idempotent matrix semiring as a sum of well-known derivations. The results of two of my articles, published in 2022, will be compared and we will draw conclusions about the advantages and disadvantages of these results. We begin by considering the nature of derivations of triangular matrices over an additively idempotent semiring R generated [...]