The Department of Geometry was founded in 1971. Its first head was Professor M.A. Sobirov. The department was headed by Associate Professor A.V. Mironov (1975-1985), Professor A.Ya. Narmanov (1990-1993), Professor A. Artikbaev (1993-2000), Professor A.Ya. Narmanov (2000-2016), and Professor R.B.Beshimov (2016-2022). Since May 25, 2016, the department has been called “Geometry and Topology”. Currently, the department is headed by Candidate of Physical and Mathematical Sciences, Associate Professor A.M. Bayturaev.
Professor M.A. Sobirov was an outstanding scholar and educator, a graduate of Moscow State University. In 1956, he co-authored the first textbook on differential geometry in the Uzbek language.
Currently, the Department of Geometry and Topology conducts research in the areas of “Foliation Theory and its Applications”, “Cardinal Properties of Topological Spaces” and “Non-Euclidean Geometry”.
The research field “Foliation Theory and Its Applications” is headed by Professor A.Y.Narmanov, Doctor of Physical and Mathematical Sciences. Professor A.Y.Narmanov was appointed head of the Department of Geometry and History of Mathematics on September 2, 2000. On December 2, 2011, this department was renamed the Department of Geometry.
A.Y.Narmanov lectures on analytic geometry, differential geometry, and topology to undergraduate mathematics students, as well as on foliation theory and an introduction to homology theory to graduate students. The department regularly hosts a research seminar under the direction of A.Y.Narmanov. Fifteen candidate dissertations and one doctoral dissertation have been defended under his supervision. A.Y.Narmanov is the author of two textbooks, a monograph, ten textbooks, and over one hundred scientific papers. Professor A.Y.Narmanov is a member of the American Mathematical Society.
The research direction “Cardinal Properties of Topological Spaces” is headed by Doctor of Physical and Mathematical Sciences, Professor R.B.Beshimov. He worked as an associate professor in the Department of Geometry at the Mirzo Ulugbek National University of Uzbekistan from 2006 to 2011. From 2016 to 2022, he served as head of the Department of Geometry and Topology. R.B.Beshimov is a scientific expert for the German journal “Zentralblatt Mathematica,” the American journals “Mathematical Reviews” and “International Journal of Mathematics and Statictics,” and the British journal “Journal of Mathematics and Computer Science.”
R.B.Beshimov lectures on differential topology and mathematics teaching methods to undergraduate students in the Faculty of Mathematics. The faculty regularly hosts a research group led by R.B. Beshimov. Five PhD theses have been defended under his supervision. R.B.Beshimov is the author of a monograph, two textbooks, and over fifty research papers.
Research in the field of “Non-Euclidean Geometry” was conducted under the supervision of Professor A.Artikbaev. Currently, research is being conducted by Professor A.S.Sharipov and his students.
Geometry & topology
Head of the department
BAYTURAYEV ASHUR MAXMADALIYEVICH
Head of Department
Degree:
Candidate of Sciences, PhD
Scientific title:
Associate Professor
Reception days:
Monday - Friday, 09:00 - 17:00
Address:
Address: 100174, Tashkent city, Almazor district, University street, 4th house
History of the department
The composition of the department
Scientific activity
The department offers master’s and doctoral programs, and over the past five years, 10 doctoral dissertations (PhD) and approximately 80 master’s theses have been successfully defended. Among the master’s students are winners of the Mirzo Ulughbeg State Scholarship and participants of the World Olympiad.
Scientific articles by students of the department are published in prestigious journals of our republic and foreign countries.
At the initiative of the department’s professors and instructors, international and national scientific conferences are held.
The department regularly hosts scientific seminars, which also feature lectures by international scholars.
The department’s research, conducted over more than half a century, has been reflected in numerous monographs and textbooks, as well as hundreds of scientific and popular science articles.
Textbooks:
- Narmanov A.Y. Differential Geometry and Topology. Bukhara, “Durdona”, 2024.
- Sharipov A.S. Analytical geometry. Tashkent, ed. “Tilsim”, 2023.
- Narmanov A.Y. Analytical Geometry. Tashkent, Innovation-Ziyo Publishing House, 2021.
- Narmanov A.Ya. Differential Geometry. Tashkent, Turon-Iqbol Publishing House, 2016.
Monographs:
- Narmanov A.Y. Geometry of Orbits of Vector Fields and Singular Foliations. Tashkent, University, 2023.
- Bayturaev A.M. Geometry of level surfaces. Tashkent, Methodist Nashriyoti Publishing House, 2023.
- Saitova S.S. Geometry of Killing vector fields. “Ma’rifat”, 2024.
- Safarova D.T. Cardinal and topological properties of covariant functors of finite degree. Т. “Ma’rifat”, 2024.
- Mukhamadiev F.G. Cardinal invariants of the space of linked systems. T, University, 2021.
- Beshimov R.B. Cardinal invariants of covariant functors in the category of topological spaces. Tashkent, University Press,
- Beshimov R.B. Weak density of topological spaces. Tashkent, University Publishing House, 2021.
Grants:
- F-4-04 Geometry and topology of foliated manifolds (supervisor: A.Y. Narmanov) (2012-2016)
- F-4-27 Study of topological and cardinal properties of some covariant functors acting on categories of topological spaces (supervisor: R.B. Beshimov) (2012-2016)
- F-4-42. Cardinal and topological properties of spaces of semi-additive tau-smooth and Radon functionals (supervisor: R.B. Beshimov) (2017-2020)
- MF-4-6. Geometry of Killing vector fields (supervisor: S.S. Saitova) (2016-2017).
- MRU-ON-2017: Development of geometric and analytical methods in control theory problems and differential games (supervisor: prof. Narmanov A.Y., 2018-2019, Uzbekistan-Russia).
- UT-OT-2020-2 “Geometric and Kinematic Invariants of T-Figures in Euclidean and Pseudo-Euclidean Spaces” (Project Leader: Academician J. Khadzhiev, 2021-2022, Uzbekistan-Turkey)
- The European Union’s Erasmus+ Programme “Key Action 1 – Mobility for learners and staff – Higher Education Student and Staff Mobility” (2020–2027). Project Coordinator: Prof. R.B. Beshimov, Uzbekistan-Greece
Currently, the Department of Geometry and Topology teaches the following subjects to undergraduate students in the specialty “60540100-Mathematics” and graduate students in the specialty “70540101-Mathematics”:
| № | Item | Brief information about the subject |
| Direction 60540100 – Mathematics | ||
| 1 | Analytical geometry | Analytical geometry is the science that studies the methods necessary for the investigation of geometric objects, namely lines and surfaces defined by algebraic functions |
| 2 | Differential Geometry and Topology | The study of differential geometry and topology develops students’ skills in applying topological methods and methods of differential calculus in the study of geometric objects |
| 3 | Differential geometry | The problem of differential geometry is to study the properties of geometric objects, that is, lines and surfaces, parameterized by differentiable functions |
| 4 | Linear algebra and analytic geometry | The course “Linear Algebra and Analytical Geometry” is an important discipline in the study of engineering, physics and technology, in solving their problems and in the analysis of mathematical models of various processes |
| 5 | Methods of teaching mathematics | The subject “Methodology of Teaching Mathematics” develops theoretical and practical knowledge and skills of students of higher educational institutions in accordance with modern requirements for teaching mathematical disciplines in secondary schools and academic lyceums |
| 6 | Differential topology | Methods of differential topology, a key area of modern mathematics, are used as a powerful tool for solving contemporary problems in algebra, mathematical analysis, differential geometry, and topology. This course plays a vital role in introducing mathematics students to contemporary areas and problems in mathematics, as well as developing their skills in applying these methods. |
| Specialty 70540101-Mathematics | ||
| 1 | Introduction to Homology Theory | This subject is one of the most important branches of modern geometry, studying knowledge about homology groups, singular homology and homology groups of topological spaces |
| 2 | Foliation theory | The goal of foliation theory is to develop students’ knowledge of the fundamentals of modern geometry, vector fields and their application to the laws of nature, as well as various processes in physics and engineering |
| 3 | Methodology of scientific research | The aim of the discipline “Methodology of scientific research” is to study the laws, principles, systems of innovative approaches, forms, methods and principles of scientific and creative activity, as well as the development of scientific research and professional competencies in postgraduate students |
International cooperation
The department’s professors and teachers regularly participate in international conferences, congresses, schools, and seminars held in countries such as Japan, Sweden, Greece, Russia, Ukraine, Kazakhstan, Turkey, and Kyrgyzstan.
The department maintains links with Moscow State University, Saint Petersburg State University, Novosibirsk State University, the Institute of Mathematics of the Academy of Sciences of the Republic of Uzbekistan, higher education institutions in all regions, the University of Warwick (UK) and Japanese universities, as well as research centers such as CIMPA and ICTP.