Scientific Laboratory of Algebra and its Applications
Laboratory Head
Jamilov Uyg’un Umurovich
Laboratory Head
📧 Email: jamilovu@yandex.ru
📞 Telefon: +998901277237
🕔 Reception days:
🏢 Office number: 310
📍 Address:
Address: 100174, Tashkent city, Almazar district, University street, house 4
More detailsAbout Laboratory
The history of the establishment of the "Algebra and its Applications" laboratory goes back to the "Mathematical Analysis and Mechanics" department, which began its activities when the Institute of Mathematics was established. The "Mathematical Analysis and Mechanics" department was established on January 16, 1944, and during 1944-1960, scientists such as N.N. Nazarov, M.T. Urazbaev, D.Kh. Karimov, I.S. Arzhanikh, M.S. Areshev, and M.F. Shulgin worked in the department.
During the early years, M.S. Areshev headed the "Mathematical Analysis and Mechanics" department, and in 1956, this department was divided into the "Mathematical Analysis" and "Theoretical Mechanics" departments. S.Kh. Sirojiddinov led the "Mathematical Analysis" department, while I.S. Arzhanikh began work as the head of the "Theoretical Mechanics" department. In the "Mathematical Analysis" department, S.Kh. Sirojiddinov served as head during 1956-1958, N.P. Romanov during 1958-1960, I.S. Arzhanikh during 1960-1980, and G.P. Matviyevskaya during 1980-1985.
By 1979, a "Functional Analysis" department was established at the Institute of Mathematics, with T.A. Sarimsoqov serving as its head during 1979-1986.
In 1986, the "Mathematical Analysis" and "Functional Analysis" departments were merged and began operating as a new department under the name "Algebra and Analysis." In the "Algebra and Analysis" department, T.A. Sarimsoqov served as department head during 1986-1988, and Sh.A. Ayupov during 1988-2018. U.A. Roziqov headed the department during 2018-2019.
In accordance with Resolution No. PQ-4387 of the President of the Republic of Uzbekistan dated July 9, 2019, "On measures for state support of further development of mathematics education and sciences, as well as fundamental improvement of the activities of the V.I. Romanovskiy Institute of Mathematics of the Academy of Sciences of the Republic of Uzbekistan," the "Algebra and Analysis" department was transformed into the "Algebra and its Applications" laboratory.
Currently, the "Algebra and its Applications" laboratory conducts scientific activities with Doctor of Physical and Mathematical Sciences, Academician Sh.A. Ayupov, Doctor of Physical and Mathematical Sciences, Academician J. Khadjiev, Doctor of Physical and Mathematical Sciences, Academician U.A. Roziqov, Doctor of Physical and Mathematical Sciences, Professor B.A. Omirov, Doctor of Physical and Mathematical Sciences, Professor I.S. Rakhimov, Doctor of Physical and Mathematical Sciences, Professor A.Kh. Khudoyberdiyev, Doctor of Physical and Mathematical Sciences, Leading Research Fellow F.M. Mukhamedov, Doctor of Physical and Mathematical Sciences, Leading Research Fellow U.U. Jamilov, Doctor of Physical and Mathematical Sciences, Leading Research Fellow F.Kh. Eshmatov, Doctor of Physical and Mathematical Sciences, Leading Research Fellow J.Q. Adashev, Doctor of Physical and Mathematical Sciences, Leading Research Fellow O.N. Hakimov, Doctor of Physical and Mathematical Sciences, Leading Research Fellow F.H. Haydarov, Doctor of Physical and Mathematical Sciences, Leading Research Fellow K.Kh. Rakhimov, Candidate of Physical and Mathematical Sciences, Senior Research Fellow R.A. Dadakhodjaev, PhD Senior Research Fellow Z.S. Bokhonov, PhD Senior Research Fellow D.E. Jumaniyozov, PhD Senior Research Fellow Q.K. Abdurasulov, and PhD Senior Research Fellow Z.H. Shermatova.
Sh.A. Ayupov was awarded the "Shuhrat" medal in 1996, the "Mehnat Shuhrati" (Labor Glory) order in 2003, and the honorary title "People's Scientist of the Republic of Uzbekistan" in 2011.
In 2017, Sh.A. Ayupov, K.K. Kudaybergenov, B.A. Omirov, and U.A. Roziqov were awarded the First Degree State Prize of the Republic of Uzbekistan.
In 2017, U.A. Roziqov received the international "Springer Nature Top Author" award, was elected as an academician of The World Academy of Sciences (TWAS) in 2018, and in 2020 won the COMSTECH international award for "Best Scientific Article" (for Rozikov U.A. Jour. Math. Biology, 2017. V.75, No.6-7, p.1715-1733).
In 2021, Sh.A. Ayupov was awarded the title "Hero of Uzbekistan" and presented with the highest decoration—the "Oltin Yulduz" (Gold Star) medal.
In 2024, Sh.A. Ayupov was awarded the title of Honorary Academician of the National Academy of Sciences of Kyrgyzstan.
In 2025, Sh.A. Ayupov and U.A. Roziqov were included in the Stanford/Elsevier Top 2% Scientists list.
In 2025, Sh.A. Ayupov was awarded the "People's Diplomat" badge.
Laboratory Staff
Scientific Activity
Currently, the "Algebra and its Applications" laboratory conducts research in the following directions:
• Operator Algebras. The operator algebras direction is an intersection of modern functional analysis and algebra theory, focused on studying deep structural and morphism problems related to locally measurable operator algebras, C*-algebras, von Neumann and Murray-von Neumann algebras. These studies provide a deeper understanding of abstract forms of operator theory, their connection with symmetric and stochastic systems, as well as algebraic analysis of mathematical physics models.
• Non-associative Algebras. The non-associative algebras direction is one of the most actively developing areas of algebra theory, where structural properties, classification, and derivation theory of Lie, Leibniz, Jordan, alternative, Poisson, and other algebras are studied. The goal of this direction is to identify new classes of non-associative algebras, describe various linear mappings in them, determine their deformations, and classify cohomological groups. Additionally, non-associative algebras are studied in connection with geometry and dynamical systems. Research results are of significant importance in developing new theoretical models in algebra, geometry, and mathematical physics.
• Dynamical Systems of Nonlinear Operators. This direction studies the long-term dynamic behavior of systems based on quadratic, cubic, and higher-order stochastic and non-stochastic operators, as well as rational mappings modeling biological, ecological, and economic processes. The main goal of the research is to analyze fixed points, periodic orbits, invariant measures, ergodic and chaotic regimes of discrete dynamics generated by operators, as well as to characterize them from the perspective of stability or bifurcation. The results not only enrich the understanding of theoretical dynamical systems but also serve as an important tool for predicting the long-term evolution of complex multi-component systems.
• Gibbs Measures. Gibbs measures are one of the fundamental concepts of modern mathematical physics, probability theory, and statistical mechanics. Such measures are widely used to describe the equilibrium state of complex systems composed of many particles. The main research conducted in this direction is devoted to constructing measures describing the state of a given physical system, examining their properties, finding ground states that minimize system energy, and identifying quantities that ensure the existence of phase transitions. The fact that Gibbs measures are currently finding applications in related fields of science demonstrates the importance of this area.
• Non-Archimedean Analysis. p-adic numbers, introduced by Kurt Hensel in the late 19th century, are today the main object of non-Archimedean analysis. In the second half of the 20th century, a major step was taken in studying p-adic numbers and their applications. In particular, non-Archimedean functional analysis and the theory of non-Archimedean dynamical systems were developed. Research conducted in these directions is mainly devoted to the theory of non-Archimedean linear operators and discrete-time dynamics of rational-fractional p-adic functions. The main problems include examining properties such as regularity or possession of periodic cycles, minimality, topological transitivity, ergodicity, and chaoticity of non-Archimedean linear operators and rational-fractional functions.
• Dynamics of Holomorphic Endomorphisms and Polynomial Mappings. In the direction of dynamics of endomorphisms and polynomial mappings, the properties of ergodic measures of endomorphisms and polynomial mappings and their applications, as well as stability in families of endomorphisms and polynomial mappings, are studied.
• Dynamics of Geodesics of Meromorphic Bundles on Riemann Manifolds. In the direction of dynamics of geodesics of meromorphic bundles, the flatness of meromorphic bundles on Riemann manifolds and the classification of omega-limit sets of geodesics of corresponding local metrics are studied.
International Cooperation
The department actively collaborates scientifically with numerous institutes and universities, including:
- University of San Diego (USA)
- University of São Paulo (Brazil)
- University of Bonn (Germany)
- Bielefeld University (Germany)
- Rhein University (Germany)
- University of Trieste (Italy)
- University of Cambridge (Great Britain)
- University of Leeds (Great Britain)
- University of Seville (Spain)
- University of Santiago de Compostela (Spain)
- University of Granada (Spain)
- University of Adelaide (Australia)
- University of Sydney (Australia)
- University of Strasbourg (France)
- Aix-Marseille University (France)
- University of Nantes (France)
- University of Paris (France)
- Kazan Federal University (Russia)
Seminars
Operator Algebras and Their Applications (scientific seminar)
Seminar venue: ZOOM ID- 7803181064
Every Monday at 14:00 at V.I.Romanovsky Institute of Mathematics, Room 105
Seminar leader: Academician Sh.A.Ayupov, seminar secretary: J.K.Adashev
Gradient Probability Measures on Lattice Systems (scientific seminar)
Seminar venue: ZOOM ID-5135322193
Every Thursday at 16:00 at V.I.Romanovsky Institute of Mathematics, Room 105
Seminar leader: Academician U.A.Rozikov, seminar secretary: O.N.Khakimov