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 [...]

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The next meeting of the Algebra and Logic Seminar will be held on October 21, 2022 (Friday) at 1:00 pm (UTC+2) online in Zoom. A talk on: Gabbay Separation for the Duration Calculus will be delivered by Dimitar Guelev (IMI - BAS). Abstract.  Gabbay's separation theorem about linear temporal logic (LTL) with past has proved to be one of the most useful theoretical results in temporal logic. Is expressive power ultimately affected, if past constructs are not allowed in the scope of future ones, or vice versa? Separation implies that it does not, and also provides a technically convenient normal form for temporal conditions. Interval Temporal Logic (ITL) and the Duration Calculus (DC) are interval-based logics. Unlike LTL, they are based on modalities which [...]

The next meeting of the Algebra and Logic Seminar will be held on October 21, 2022 (Friday) at 1:00 pm (UTC+2) online in Zoom. A talk on: Ranks and Presentations for Order-Preserving Transformations with One Fixed Point will be delivered by Jörg Koppitz (joint work with S. Worawiset). Abstract. We consider the semigroup (no monoid) of all order-preserving full transformations α on an n-element chain Xn = {1 < 2 …< n}, where p is the only fixed point in α, for some given p ∈Xn, denoted by On,p. This semigroup is nilpotent. In particular, the semigroup On,1 (i.e. p = 1) is already well studied, since it is the maximal nilpotent subsemigroup of the Catalan monoid. But the semigroup On,p is still not well [...]

The next meeting of the Algebra and Logic Seminar will be held on October 14, 2022 (Friday) at 1:00 pm (UTC+2) in Room 578 of IMI - BAS and online in Zoom. A talk on: Families of triple coverings of algebraic curves will be delivered by Hristo Iliev (American University in Bulgaria and IMI - BAS). Abstract. The talk is a continuation of my previous talk "Examples of non-reduced components of the Hilbert scheme of smooth projective curves using ruled surfaces" that I gave on August 19, 2022. In the present talk we consider curves that are triple covers of smooth projective curves of genus γ ≥ 0. We obtain families of curves on smooth surface scrolls which, under suitable numerical assumptions, yield components of [...]

The next meeting of the Algebra and Logic Seminar will be held on September 23, 2022 (Friday) at 1:00 pm (UTC+2) in Room 578 of IMI - BAS. A talk on: Geometry and logic in quantum computations will be delivered by Nikolay M. Nikolov (INRNE - BAS). Abstract. In 1936, Garrett Birkhoff and John Von Neumann published one of the most general axiomatic foundations of Quantum Theory, which has become known to this day as "Quantum Logic" (Annals of Mathematics, vol. 37 (1936) 823-843). In this work, they start from an ortho-modular lattice that serves as a model of the partially ordered set of all quantum events. They also found a connection with Projective Geometry. The main case of geometries is on complex numbers, but [...]