Project title: Irregular sets in Dynamical Systems
Project IRN: AP08051987
The aim of the project is to carry out scientific research in the field of dynamical systems and make contributions to the development of fundamental science and train young scientists in the field. Preliminary joint experimental research of PI with the team members provides evidence that many interesting new findings can be obtained the field of dynamical systems. With the present project, we aim to provide rigorous and mathematically valid proofs for our experimental initial analysis of irregular sets.
(Proposed time of project beginning and its duration: 1 January 2020 – 31 December 2022, 3 years.)
Publications:
- Kadyrov, S., Kashkynabayev, A., Skrzypacz, P., Kaloudis, K., Bountis, A. Periodic solutions and the avoidance of pull-in instability in nonautonomous microelectromechanical systems. Mathematical Methods in the Applied Sciences
DOI: https://doi.org/10.1002/mma.7725 - Kadyrov, S., & Mashurov, F. (2021). Generalized continued fraction expansions for π and e. Journal of Discrete Mathematical Sciences and Cryptography, 1-11.
DOI: https://doi.org/10.1080/09720529.2021.1936897 - Kadyrov, S., & Mashurov, F. (2021). Unified computational approach to nilpotent algebra classification problems.Communications in Mathematics, 29,
DOI: https://doi.org/10.2478/cm-2021-0019 - Mashurov, F., & Kaygorodov, I. (2020). One-generated nilpotent assosymmetric algebras. Journal of Algebra and Its Applications, 2250031.
DOI: https://doi.org/10.1142/S0219498822500311 - N. Aitu, Kadyrov, S. (2020). Survivor sets in subshifts of finite type, Kazakh Mathematical Journal, 20(2), 54-62
URL: http://www.math.kz/media/journal/journal2020-07-2123165.pdf
Project title: Asymptotic problems in algebraic combinatorics
Project IRN: AP08051987
Algebraic combinatorics deals with rich structures arising in connections with algebras, groups, representation theory, algebraic geometry and other fields of mathematics. Most objects and problems arising in algebraic combinatorics are usually studied from pure algebraic, enumerative, or geometric perspectives but not asymptotically. Besides some classical problems such as large dimensions of irreducible representations of the symmetric group, the area has recently faced many new open challenging problems. Some of them were initiated and posed by R. Stanley, e.g. problems on asymptotic behavior of largest Littlewood-Richardson coefficients and limits of specializations of Schubert polynomials. In this project, we address these and other closely related problems.
We aim to study certain fundamental asymptotic and probabilistic questions related to combinatorial objects arising in algebraic combinatorics, representation theory, algebraic geometry and in particular, Schubert calculus and combinatorial K-theory. As we have already mentioned, these objects were previously studied mostly non-asymptotically from algebraic or geometric perspective and this area has many open problems of asymptotic nature. Interest in these questions is growing due to connections with various fields.
More specifically, we address several concrete problems of asymptotic and probabilistic nature arising in algebraic combinatorics and related fields, especially in combinatorial K-theory.
2020-2021 published papers:
- D. Yeliussizov, Positive specializations of symmetric Grothendieck polynomials, Advances in Mathematics, Vol. 363, 2020, Article 107000, 35 p
https://doi.org/10.1016/j.aim.2020.107000 - D. Yeliussizov, Dual Grothendieck polynomials via last-passage percolation, Comptes Rendus Mathematique Acad. Sci. Paris, Vol. 358. 2020, 497–503.
https://doi.org/10.5802/crmath.67 - D. Yeliussizov, Enumeration of plane partitions by descents, Journal of Combinatorial Theory Series A, Vol. 178, 2021, Article 105367, 18 p.
https://doi.org/10.1016/j.jcta.2020.105367 - D. Yeliussizov, Random plane partitions and corner distributions, Algebraic Combinatorics, Vol. 4, 2021, 599–617.
https://doi.org/10.5802/alco.171
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