# Faculty Mentors at the Institute of Mathematics

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**Academician Shavkat Ayupov**

###### Director, Institute of Mathematics, Uzbekistan Academy of Sciences

Lead Mentor for the IRES Program

Shavkat Ayupov is a well-known mathematician, doctor of physical and mathematical sciences, professor, academician, distinguished scientist of Uzbekistan. He is one of the leaders of the modern scientific school of functional analysis and algebra, and made a great contribution to the development of science and education in Uzbekistan.

Ayupov graduated with honors from the Mechanics and Mathematics Department of Tashkent State University (now the National University of Uzbekistan) in 1974 and began his postgraduate studies in Functional Analysis under the supervision of Academician T.A. Sarymsakov and Professor J. Khadzhiev. In 1977 he defended his thesis on "Tikhonov rings, their homomorphisms and modules".

In 1979, Ayupov started working at the Institute of Mathematics of the Uzbekistan Academy of Sciences as a senior researcher in the Functional Analysis division, where he began active research on the theory of operator algebras and quantum probability theory. He took his research in a new direction - the theory of ordered Jordan algebras, its applications to non-associative integration and probability theory. He investigated the connections between the types of Jordan algebras of self-adjoint operators (JW-algebras) and their enveloping von Neumann algebras. He obtained results on the extension of traces from the JW-algebra to the complex enveloping von Neumann algebra, and on the representation of an abstract ordered Jordan algebra as an algebra of unbounded self-adjoint operators affiliated with a JW-algebra.

In June 1983, Ayupov successfully defended his doctoral thesis on "Classification, representation and probabilistic aspects of ordered Jordan algebras". Simultaneously, he conducted research on the Lie structure in von Neumann algebras, and on the theory of real operator algebras. In 1994, Ayupov was visiting professor at the Louis Pasteur University in Strasbourg (France) collaborating with Professor J. L. Loday. After this trip, Ayupov began research on the theory of Leibniz algebras, which are a "non-antisymmetric" generalization of Lie algebras. In this field, he obtained deep, purely algebraic results on the structural theory and classification of finite-dimensional simple and nilpotent Leibniz algebras.

In 2000, Ayupov initiated research on the theory of derivations in operator algebras, which represent an important mathematical apparatus of quantum dynamics. He obtained significant results concerning the automatic continuity, innerness and spatiality of derivations in the algebras of unbounded operators. Ayupov's research is a major contribution to the development of the theory of operator algebras and abstract non-associative algebra, and his acheivements have been recognized by many leading scientists worldwide. He is the author of 6 monographs (2 of which were published in Holland, one in the USA), 5 textbooks and teaching aids for students of mathematical specialties of higher education institutions, more than 300 scientific articles, most of which are published in international peer-reviewed journals. In 1989 he was elected a corresponding member, and in 1995 a full member (Academician) of the Uzbekistan Academy of Sciences. Ayupov is also a member of the American Mathematical Society since 1980.

Ayupov is a talented manager of science and education in Uzbekistan. During 1992-1997 and since 2004 he has been the Director of the Institute of Mathematics of the Uzbekistan Academy of Sciences. From 1997-2003 he was the Chairman of the Higher Attestation Commission under the Cabinet of Ministers of the Republic of Uzbekistan; from 2003-2004 he was Deputy Minister of Higher and Secondary Special Education. He is the editor-in-chief of the "Uzbek Mathematical Journal" and of the scientific and methodical journal "Physics, Mathematics and Informatics" for students of lyceums and colleges. Ayupov made great contributions to the training of young scientific minds. Under his direct supervision, 35 Ph.D. and 10 Doctor of Science dissertations were defended.

Ayupov is an active participant and organizer of many international scientific conferences. He took part in the International Congress of Mathematicians in Kyoto (Japan, 1990), Zurich (Switzerland, 1994), Berlin (Germany, 1998), Beijing (China, 2002), and Seoul (South Korea, 2014) as well as in conferences on algebra and functional analysis In Germany (1980, 1988, 1992), Romania (1982), Great Britain (1986, 2004), Italy (1987, 2004, 2009), Spain (1993, 2000, 2012), France (1994, 2001), USA (2014), and Mexico (2008). He was the chairperson and/or a member of the organizing committee of the following international conferences in Tashkent: “Nonassociative algebra” (1993), the Uzbek-French conference “Algebra and Operator Theory” (1997), "Operator Algebras and Quantum Probability" (2005), “Operator Algebras and Related Topics” (2012), “Algebra, Analysis and Quantum Probability” (2015), as well as the USA-Uzbekistan Conference on “Analysis and Mathematical Physics” at California State University, Fullerton (2014). In 2002-2011, he was a coordinator of a joint project with the Institute of Applied Mathematics of the University of Bonn. Ayupov, together with a group of students, conducted research at the University of Bonn annually from 2002-2011. From 2008-2013, he was a senior associate at the Center for Theoretical Physics (ICTP) in Trieste. Italy.

Ayupov was awarded the "Shukhrat" medal in 1996, the "Mehnat Shuhrati" order in 2003, the honorary title "Distinguished Scientist of the Republic of Uzbekistan" in 2011, and State Prize of Uzbekistan in 2017, which is the highest honor bestowed upon scientists in Uzbekistan, for his contributions in the development of mathematical sciences and education and, his fruitful pedagogical activities and training of young generations of scientists in Uzbekistan.

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**Academician Shavkat Alimov**

### Institute of Mathematics, Uzbekistan Academy of Sciences

Mentor for the IRES Program

Shavkat Alimov is a prominent mathematical physicist whose major work focuses on spectral theory of operators and solutions of boundary value problems in mathematical physics. He is the author of more than 150 mathematical works in mathematical physics, partial differential equations, spectral theory; most of them were published in international journals and conference proceedings. He is a member of the Editorial Board of Eurasian Mathematical Journal (Kazakhstan), the Uzbek Mathematical Journal (Uzbekistan), the Journal of Pure and Applied Mathematics (Azerbaijan), the Journal of Contemporary Analysis and Applied Mathematics (Turkey). Dr. Alimov is a member of the International Academy of Sciences of Higher Education (Russia). Dr. Alimov was an invited speaker at the fourth International Conference "Inverse problems: Modeling and Simulation" (2008) in Turkey, at the International Conference "Modern Problems of Computational Mathematics and Mathematical Physics" (2009) in Moscow and at the seventh Congress of the International Society for Analysis, its Applications and Computation, (2009) in London.

Dr. Alimov received his M.Sc. in Physics (1968), PhD in Mathematics (1970) and Doctor of Sciences in Physics and Mathematics (1973), all from Moscow State University. He was Professor of Mathematics at the Moscow State University (Department of Computational Mathematics) from 1970 to 1984. Since 1984, he has been a Professor of Mathematics at the National University of Uzbekistan and since 2006, a Professor of Mathematics at the Tashkent Branch of the Moscow State University. From June 2012 to September 2017, he was the Head of Mathematical Modeling Laboratory at MIMOS (Malaysian Institute of Microelectronics, Kuala Lumpur, Malaysia). He has been a member of the Academy of Sciences of Uzbekistan since 1985 the same year in which he was awarded the Uzbekistan State Prize, named after Beruni. He was the rector of Samarkand State University (1985-1987) and the National University of Uzbekistan (1987-1990). He was a visiting researcher/professor at the Waseda University (Tokyo, Japan) in 1977, at the Eötvös Loránd University (Budapest, Hungary) in 1983, at the University of Mainz (Mainz, Germany) in 1991, at the University of Bonn (Bonn, Germany) in 2005-2007, and at California Institute of Technology (2000-2001).

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**Academician Ravshan Sabirov **

###### Dr. Sabirov is the director of the Institute of Biophysics and Biochemistry at the National University of Uzbekistan, and Chief Scientist of the Laboratory of Molecular Physiology

###### Lead Mentor for the IRES Program

Research interest of the Laboratory: ion channels and transporters, their biophysical characterization and their role in basic physiological function of living cells. The Laboratory has long been studying the basic principles of cell volume regulation under osmotic stress. When cells experience an osmotic challenge (such as hypotonic stress), they first passively swell. If this swelling persists, the cells would die. However, cells start actively regulate their volume trying to bring it back to normal level. This is accomplished by activation of a number of ion channels and transporters, which extrude the osmolytes (small osmotically active molecules and inorganic ions, like potassium, calcium and chloride), Water follows the efflux of osmolytes and cell shrinks and survives. Our main interest is the role of anion-selective channels (called volume-regulated anion channels) in cell volume regulation. We study their basic biophysical properties using electrophysiological techniques (such as patch-clamp and lipid bilayers) and role in volume regulation in immune cells using light transmittance detection.

The Laboratory staff consist of two seniour scientists, three young researchers and one technician. We also have several Ph.D. students, masters student and undergraduate students.

## RESEARCH PROJECTS/TOPICS FOR STUDENTS

- Biophysical profile of the maxi-anion channel in melanoma cells cultured in different media.
- Effect of biologically active preparations (substances or plant extracts) on the volume regulation of rat thymocytes under hypoosmotic stress.
- Effect of biologically active preparations (substances or plant extracts) on the volume-regulated anion channels in cultured cells.
- Modeling of the volume-sensitive outwardly rectifying (VSOR) anion channel as a hexamer of LRRC8 proteins and searching for drug-binding pockets.

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**Dr. Ahmedov Bobomurat**

Dr. Ahmedov is the Head of the Department of Astrophysics. Lead Mentor for the IRES Program

The main research works are devoted to

the Relativistic Astrophysics including the general-relativistic electrodynamics of continuous media and its application for theoretical explanation and analysis of EM (electromagnetic), GW (gravitational waves), optical and astrophysical processes in the external gravitational fields of compact gravitational objects as rotating and oscillating neutron stars and various black holes. Experimental tests of general relativity, general relativistic EM effects and fields for pulsars and magnetized rotating and oscillating neutron stars, quasinormal modes, shadow and energetics of black holes, gravitational lensing are also among my scientific interests. In addition, we carry out a research on VLF (very low frequency) and GPS EM waves propagation in Earth ionosphere and study the ionospheric disturbances caused by various atmospheric, terrestrial and extraterrestrial phenomena.

The Laboratory staff consist of two senior scientists, three young researchers (Ph.D.) and several Masters and undergraduate students.

## RESEARCH PROJECTS/TOPICS FOR STUDENTS

- Study of motion of charged particles around black holes in the presence of external magnetic field
- Investigation of the effective potential for a charged particle and the particles with no vanishing magnetic momentum, orbiting around the black hole, as a function of strength of external magnetic field, electric charge, magnetic momentum, rotating parameter of black hole
- Study the exact expression for the dependence of the radius of an innermost stable circular orbit from the electric charge and magnetic momentum of the particles in the equatorial plane of the black holes in the AGT in magnetic field
- Derivation of the capture cross section of test particles with electric charge and magnetic momentum by a black hole in external magnetic field
- Exact rotating black hole solutions in modified theories of gravity and in the higher dimensions
- Analytical models describing collapse and exotic compact objects in Quantum Gravity
- Optical and energetic properties of black holes
- Plasma magnetosphere of rotating and oscillating magnetized neutron stars.

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**Dr. Utkir Rozikov **

###### Deputy Director for Research, Institute of Mathematics, Uzbekistan Academy of Sciences. Mentor for the IRES Program.

Doctor of Sciences in Mathematics, Institute of Mathematics, Uzbekistan Academy of Sciences, 2001.

Ph.D. in Mathematics, Institute of Mathematics, Uzbekistan Academy of Sciences, 1995.

M.S. in Mathematics, Samarkand State University, 1993.

#### Research Interests

Gibbs measures, dynamical systems, statistical mechanics, non-linear dynamical systems in mathematical biology.

### Dr. Bakhrom Omirov

###### Head of Faculty, Algebra and Functional Analysis, National University of Uzbekistan and Senior Scientific Fellow, Institute of Mathematics, Uzbekistan Academy of Sciences. Mentor for the IRES Program.

Doctor of Sciences in Mathematics, Institute of Mathematics, Uzbekistan Academy of Sciences, 2006.

Ph.D. in Mathematics, Institute of Mathematics, Uzbekistan Academy of Sciences, 2000.

M.S. in Mathematics, Novosibirsk State University, 1993.

#### Research Interests

Non-associative algebras and structure theory of Leibniz algebras.

### Dr. Abror Khudoyberdiyev

###### Senior Scientific Fellow, Institute of Mathematics, Uzbekistan Academy of Sciences. Mentor for the IRES Program.

Doctor of Sciences in Mathematics, Institute of Mathematics, Uzbekistan Academy of Sciences, 2016.

Ph.D. in Mathematics, Institute of Mathematics, Uzbekistan Academy of Sciences, 2010.

M.S. in Mathematics, National University of Uzbekistan, 2007.

#### Research Interests

Nilpotent Leibniz super algebras and degenerations of varieties of Algebras.

### Dr. Farkhod Eshmatov

###### Visiting Researcher, Institute of Mathematics, Uzbekistan Academy of Sciences. Mentor for the IRES Program.

Ph.D. in Mathematics, Cornell University, 2007.

M.S. in Mathematics, State University of New York at Binghamton, 2000.

#### Research Interests

Algebraic topology and homological algebras.

### Dr. Erkinjon Karimov

###### Senior Researcher, Institute of Mathematics, Uzbekistan Academy of Sciences. Mentor for the IRES Program.

Ph.D. in Mathematics, National University of Uzbekistan, 2006.

M.S. in Mathematics, Fergana State University, 1998.

#### Research Interests

Direct and inverse problems for integer and fractional PDE and special functions in fractional PDE.

### Dr. Rustam Turdibaev

Scientific Fellow, Institute of Mathematics, Uzbekistan Academy of Sciences. Mentor for the IRES Program.

Ph.D. in Mathematics, University of Santiago de Compostela, 2015.

M.S. in Mathematics, National University of Uzbekistan, 2010.

#### Research Interests

Leibniz cohomology in low degrees and structure theory of Leibniz n-algebras.

### Dr. Yulduzoy Djumaniyazova

Assistant Professor, Urgench State University. Mentor for the IRES Program.

Ph.D. in Agriculture, Institute of Soil Science and Agrochemistry, Uzbekistan Academy of Sciences, 2011.

M.S. in Environmental Protection, Tashkent Institute of Irrigation and Melioration, 2005.

#### Research Interests

Plant physiology, plant science, agrochemistry and microbiology.

### Dr. Javlon Rayimbaev

Junior Researcher, Institute of Astronomy, Uzbekistan Academy of Sciences. Mentor for the IRES Program.

Ph.D. in Physics, Instititute of Astronomy, Uzbekistan Academy of Sciences, 2020.

M.S. in Physics, National University of Uzbekistan, 2013.

#### Research Interests

Electrodynamics, relativistic astrophysics and general relativity.

### Dr. Gayrat Urazboev

Professor, Urgench State University. Mentor for the IRES Program.

Doctor of Science in Mathematics, National University of Uzbekistan, 2007.

Ph.D. in Mathematics, Institute of Mathematics, Uzbekistan Academy of Sciences, 2001.

M.S. in Mathematics, Moscow State University, 1992.

#### Research Interests

Inverse scattering method, nonlinear evolution PDE with self-consistent source, solitons theory, integrability.