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 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 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 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 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 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 23, 2023 (Friday) at 1:00 pm 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 Borisov. Abstract   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 online in Zoom on September 29, 2023 (Friday) at 1:00 pm (UTC+2). A talk on: Reset Controller Synthesis will be delivered by Naijun Zhan (Institute of Software Chinese Academy of Sciences (ISCAS), China). Abstract. Controller synthesis provides a Correct-by-construction mechanism to guarantee the correctness and reliability of hybrid systems (HS) by design. Depending on the types of controls, controllers can be classified into reset controllers, feedback controllers, and switching logic controllers. Reset controllers steer the behaviour of a HS to attain system objective through restricting its initial set and redefining the reset map associated with discrete jumps, which is less explored in the literature, although it is of theoretical and practical significance. In this [...]

The next meeting of the Algebra and Logic Seminar will be held in hybrid format (in Room 578 of IMI and online via Zoom) on October 13, 2023 (Friday) at 1:00 pm (UTC+3). A talk on: Emmy Noether’s Theorem on the Finite Generation of the Algebra of Invariants will be delivered by Marin Genov (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences). Abstract. I will introduce Emmy Noether’s theorem on the finite generation of invariants and give two proofs of it. As an example, I will also calculate the algebra of invariants of the dihedral group of order 2n acting on C[x,y]. Link to the Zoom room: https://us02web.zoom.us/j/85137375021?pwd=RE5QczdFTE1xL1R6MnI2b1lkcGczQT09 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 in hybrid format (in Room 578 of IMI and online via Zoom) on October 20, 2023 (Friday) at 1:00 pm (UTC+3). A talk on: Prime numbers and random walks in a square grid will be delivered by Alberto Fraile (Czech Technical University in Prague, Czech Republic). Joint work with Osame Kinouchi, Prashant Dwivedi, Roberto Martínez, Theophanes E. Raptis, and Daniel Fernández Abstract. One can argue that prime numbers present perplexing features, in a hybrid of local unpredictability and global regular behavior. It is this interplay between randomness and regularity that motivated searches for both local and global patterns that could potentially become signatures for certain underlying fundamental mathematical properties.In recent years, computer simulations [...]

The next meeting of the Algebra and Logic Seminar will be held online via Zoom on November 3, 2023 (Friday) at 1:00 pm (UTC+2). A talk on: A Reduction of Temporary Coalitions in Infinite Multiplayer Games will be delivered by Dimitar Guelev (IMI-BAS, Bulgaria). Abstract.We propose a transformation of Concurrent Game Models which enables the reduction of infinite multiplayer games where players can form temporary coalitions to games with no coalitions by extending moves to include the negotiation steps that lead to the formation of coalitions. We adopt conditional promises as the building blocks of negotiation. Temporary coalitions and their agendas arise as the logical consequences of mutual promises. The transformation enables the use of established solution concepts about games with no coalitions for [...]

The next meeting of the Algebra and Logic Seminar will be held in hybrod format (in Room 578 of IMI - BAS and online via Zoom) on November 10, 2023 (Friday) at 1:00 pm (UTC+2). A talk on: Transfinite version of the Mittag-Leffler condition for the vanishing of the derived limit will be delivered by Mishel Carelli (Technion – Israel Institute of Technology, Israel). Abstract.We give a necessary and sufficient condition for an inverse sequence  S0 ← S1 ← . . . indexed by natural numbers to have lim¹S = 0. This condition can be treated as a transfinite version of the Mittag-Leffler condition. We consider inverse sequences in the category of abelian groups. We also show that the class of inverse sequences S [...]

The next meeting of the Algebra and Logic Seminar will be held in hybrod format (in Room 578 of IMI - BAS and online via Zoom) on November 17, 2023 (Friday) at 1:00 pm (UTC+2). A talk on: Noncommutative invariants of dihedral groups will be delivered by Boyan Kostadinov (IMI - BAS, Bulgaria). Abstract. We consider the 2-generated free metabelian associative and Lie algebras over the complex field and the invariants of the dihedral groups of finite order acting on these algebras. In the associative case we find a finite set of generators of the algebra of invariants. In the Lie case, when the algebra of invariants is not finitely generated, we give a minimal system of generators of the invariants in the commutator [...]

The next meeting of the Algebra and Logic Seminar will be held online on November 24, 2023 (Friday) at 1:00 pm (UTC+2) with two talks. At 1:00 pm (UTC+2) Dimitrinka Vladeva (IMI - BAS) will deliver a talk on Catalan numbers and additively idempotent semirings At 2:00 pm (UTC+2) Roussanka Loukanova (IMI - BAS) will deliver a talk on Semantics of Propositional Attitudes in Type-Theory of Algorithms Title: Catalan numbers and additively idempotent semirings Abstract. The purpose of the present talk is to provide new applications of remarkable Catalan numbers. In Richard Stanley’s book Enumerative Combinatorics, Volume II (Cambridge University Press) there are many combinatorial objects that are counted by the Catalan numbers as well as applications in graph theory, Young diagrams, lattice theory, real matrices, [...]