семинар Алгебра и логика

На 2 юли 2021 г. (петък) от 13:00 часа ще се проведе дистанционно заседание на семинара по „Алгебра и логика”. Доклад на тема Noncommutative Poisson structures, Hochschild type complexes and Gröbner bases theory ще изнесе Natalia Iyudu (Lancaster University, UK). Абстракт: 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 paper, based on arguments [...]

На 9 юли 2021 г. (петък) от 13:00 часа ще се проведе дистанционно заседание на семинара по „Алгебра и логика”. Доклад на тема The mysterious Kronecker coefficients of the Symmetric group ще изнесе Greta Panova (University of Southern California, USA). Абстракт. 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 general linear group. Despite [...]

На 16 юли 2021 г. (петък) от 13:00 часа ще се проведе дистанционно заседание на семинара по „Алгебра и логика”. Доклад на тема Proof Complexity of Resolution over linear inequalities ще изнесе Stefan Dantchev (Durham University, United Kingdom). Абстракт. 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 of SP will be [...]