An online session of the Algebra and Logic Seminar will be held on June 24, 2022 (Friday) at 1:00 pm (UTC+3). A talk on: Dependent-Type Theory of Situated Information with Context Assessments will be delivered by Roussanka Loukanova. Abstract. I shall introduce an enriched formal language of information that establishes propositions dependent on situations and types. The types can be basic or complex. Complex propositional types are defined recursively. The language supports structured data of situated information, which can be partial, parametric, and underspecified. Information can be associated with quantitative evaluations depending on situations. The formal terms can integrate propositional types of situated information with statistical and other quantitative evaluations. Structured content integrated with quantitative data facilitates development of new techniques for amalgamating logic representation [...]

An online session of the Algebra and Logic Seminar will be held on June 10, 2022 (Friday) at 4:00 pm (UTC+3). A talk on: Computing Eigenvectors of Symmetric Tridiagonals with the Correct Number of Sign Changes will be delivered by Plamen Koev (San José State University, USA). Abstract. The symmetric tridiagonal eigenvector problem has been a central research topic in numerical linear algebra since its inception. Of the myriad of algorithms today, none is provably optimal and accurate at the same time. “Optimal” means, a subset of k eigenvectors is computed in O(kn) time. “Accurate” means that the computes eigenvectors are orthogonal and satisfy the typical relative gap error bound. In this talk, we focus our attention on a neglected oscillating property of the eigenvectors: [...]

An online session of the Algebra and Logic Seminar will be held on May 20, 2022 (Friday) at 4:00 pm (UTC+3). A talk on: Bootstrap percolation: merging operations for polytopes will be delivered by Ivailo Hartarsky (Université Paris-Dauhpine, PSL, France, visiting scholar at Instituto de Matemática Pura e Aplicada, Rio de Janeiro, Brazil). Abstract. Bootstrap percolation is a group of statistical physics models intensively studied since the 1970s in mathematics, physics, computer science, as well as social sciences. They are cellular automata generalising the following paradigmatic example. Arbitrarily declare some sites of Z^2 initially infected. Iteratively, at each discrete-time round, additionally infect each site with at least 2 infected neighbours. The last decade has seen the accomplishment of a full classification of all such [...]

An online session of the Algebra and Logic Seminar will be held on May 13, 2022 (Friday) at 1:00 pm (UTC+3). A talk on: A counterexample to the modular isomorphism problem will be delivered by Diego García-Lucas (Universidad de Murcia, Spain). Abstract. The modular isomorphism problem asks whether the isomorphism type of the modular group algebra of a p-group G over a field of characteristic p determines the isomorphism type of G. It was explicitly mentioned in a survey by Richard Brauer in 1963, and was the only classical version of the isomorphism problem for group rings which had resisted a solution, though it received considerable attention. Several partial positive solutions were obtained imposing very strong conditions on the group G, for instance the [...]

An online session of the Algebra and Logic Seminar will be held on April 29, 2022 (Friday) at 4:00 pm (UTC+3). A talk on: Images of multilinear polynomials on upper triangular matrices will be delivered by Thiago Castilho de Mello (Universidade Federal de São Paulo, Brazil). Abstract.  Let f(x1, …, xm) be a polynomial in noncommutative variables over an infinite field K. If A is a K-algebra, it defines in a natural way a map Am → A. If the polynomial f is multilinear, the famous Lvov-Kaplansky conjecture asks whether the image of a multilinear polynomial on a matrix algebra is a vector subspace. Solutions to this problem are known only for n = 2 or m = 2 with partial results for m = 3 and n = 3. In this talk, we [...]

An online session of the Algebra and Logic Seminar will be held on April 15, 2022 (Friday) at 1:00 pm (UTC+3). A talk on: Quantisation of free associative dynamical systems. Bi-quantum structure of the stationary KdV hierarchy. Non-deformation quantisation of the Volterra hierarchy will be delivered by Alexander V. Mikhailov (University of Leeds, UK). Abstract. Traditional quantisation theories start with classical Hamiltonian systems with variables taking values in commutative algebras and then study their non-commutative deformations, such that the commutators of observables tend to the corresponding Poisson brackets as the (Planck) constant of deformation goes to zero. I am proposing to depart from dynamical systems defined on a free associative algebra A. In this approach the quantisation problem is reduced to the problem of finding [...]

An online session of the Algebra and Logic Seminar will be held on April 1, 2022 (Friday) at 1:00 pm (UTC+3). A talk on: Automorphisms of simple quotients of the Poisson and universal enveloping algebras of sl_2 will be delivered by Altyngul Naurazbekova (L. N. Gumilyov Eurasian National University, Nur-Sultan, Kazakhstan). Abstract. Let P(sl_2(K)) be the Poisson enveloping algebra of the Lie algebra sl_2(K) over an algebraically closed field K of characteristic zero. U. Umirbaev, V. Zhelyabin proved that the quotient algebras P(sl_2(K))/(C_P - λ), where C_P is the standard Casimir element of sl_2(K) in P(sl_2(K)) and 0 ≠ λ ∈K, are simple. Using a result by L. Makar-Limanov on groups of automorphisms of a class of surfaces, we describe generators of the automorphism group [...]

An online session of the Algebra and Logic Seminar will be held on March 25, 2022 (Friday) at 1:00 pm (UTC+2). A talk on: An Application of Separation in Discrete Time Interval Temporal Logic to Branching Time will be delivered by Dimitar Guelev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences). Abstract. In this talk we make an application of our separation theorem for discrete time Interval Temporal Logic (ITL) to the study of Interval-based Computation Tree Logic (ICTL*). We prove that the expressibility of the expanding modalities and, most importantly, propositional quantification, carry over from linear time ITL to the branching time system of ICTL*. The relevance of this follows from the fact that point-based propositionally quantified CTL* (QCTL*) is the established intermediate [...]

An online session of the Algebra and Logic Seminar will be held on March 18, 2022 (Friday) at 4:00 pm (UTC+2). A talk on: Absorbing ideal structures of commutative rings will be delivered by Ece Yetkin Celikel (Hasan Kalyoncu University, Turkey). Abstract. Let R be a commutative ring with nonzero identity. As generalizations of prime ideals, the absorbing ideals were first defined and studied by A. Badawi in 2007. A proper ideal I of R is said to be 2-absorbing if whenever a, b, c ∈ R with abc ∈ I, then either ab ∈ I or ac ∈ I or bc ∈ I. After this date, many researches have been done to introduce various extensions of this concept. In this talk, we present [...]

An online session of the Algebra and Logic Seminar will be held on March 11, 2022 (Friday) at 2:00 pm (UTC+2). A talk on: Multi-summation in difference rings and applications will be delivered by Carsten Schneider (Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria). Abstract. Symbolic summation in difference fields started with Karr's summation algorithm (1981) which can be considered as the discrete version of Risch's indefinite integration algorithm in differential fields. In the last 20 years this approach has been generalized and enhanced to a constructive summation theory of difference rings. In general, one can represent algorithmically any expression in terms of indefinite nested sums defined over hypergeometric products in such rings. As a crucial by-product one obtains optimal representations where the [...]