Utkir Rozikov

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Utkir Rozikov
File:Utkir Rozikov.jpg Utkir Rozikov.jpg
Born	(1970-05-20) May 20, 1970 Bukhara, Uzbekistan
🏡 Residence	Tashkent, Uzbekistan
🏳️ Nationality	Uzbek
💼 Occupation

Utkir Abdulloyevich Rozikov (born May 20, 1970) is an internationally renowned expert in probability, mathematical physics and analysis, specializing in dynamical systems and statistical mechanics on graphs. He represents the strong Tashkent research school which grew from the Dobsrushin–Minlos–Sinai seminar at Moscow in the 1960–70s. Rozikov has made significant contributions to the deep analysis of Gibbs states in topical models of statistical mechanics on trees (Ising, Potts, SOS), in particular with random interactions and/or in external field. He has promoted new tools in studying Gibbs measures on graphs, such as group representation theory, information flows, node-weighted random walks, contour methods on trees, and non-linear analysis. Rozikov has also advanced the idea of studying p-adic dynamical systems relevant to multiscale and/or chaotic systems, applied to statistical mechanics on trees and Cayley graphs of non-amenable groups. His more recent interests are focussed on evolution algebras of sex-linked populations, aiming to incorporate thermodynamics in mathematical biology models. [1]

Utkir Rozikov was elected as a member of The World Academy of Sciences (TWAS) in 2018.

Biography

Utkir Abdulloyevich Rozikov was born into Uzbek family on May 20, 1970, in Bukhara, Uzbekistan. He is a professor in the Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent, Uzbekistan. He was graduated the Samarkand State University (1993) with an honour diploma. He was a winner of several Mathematical Olympiads. He got Ph.D (1995) and Doctor of sciences in physics and mathematics (2001) degrees from the Institute of Mathematics, Tashkent. He is professor since 2010.

Rozikov (since 1995) has published over 140 papers in top journals including 11 papers in the flagship Journal of Statistical Physics (Impact Factor 1.202) and also in Lett. Math. Phys. (1.939), Comm. Math. Phys. (2.086), J. Stat. Mech. Theory Exp. (2.404), J. Math. Anal. Appl.  (1.120), etc. In particular, in 2013 he published an extensive review paper (112 pages) in Rev. Math. Phys. (1.329), followed by the authoritative research monograph “Gibbs Measures on Cayley Trees” (World Scientific, 2013). [2]

Rozikov was a visiting professor and invited researcher at many universities and research centres in France, Germany, Italy, Spain, UK, Switzerland and Turkey.

Research interests

1. Gibbs measures of lattice models of statistical mechanics.
2. p-adic Gibbs measures in the field of p-adic numbers.
3. Random walks in a random environment on the metric spaces.
4. The dynamical systems and processes generated by nonlinear operators.
5. Von Neumann algebras associated with a limit Gibbs state of certain models of quantum statistical mechanics.
6. p-adic dynamical systems.
7. Harmonic and p-harmonic functions on graphs.
8. Evolution and genetic algebras.

Awards and fellowships [3]

• (1995) Prize of Japan Embassy in Tashkent.
• (2001) Prize winner among young scientists of Academy Sciences of Uzbekistan.
• (2001) Prize of The World Academy of Sciences (TWAS) and Uzbekistan Academy of Sciences.
• (2002) Grantee of Cambridge colleges hospitality scheme.
• (2002) Grantee for ICM-2002, Beijing, China.
• (2002, 2004) Fellowship grants received from ICTP, Trieste, Italy (3 months each)
• (2003) Grantee for NATO-Advanced Studies, Edinburgh, UK
• (2003) Medal "Uzbekiston Belgisi" from government of Uzbekistan.
• (2003, 2006, 2012) Fellowship grant received from IHES, Bures-sur-Yvette, France (4
• months, 2 months and 3 months durations).
• (2003-2006) NATO Reintegration Grant (3 years duration)
• (2004) The Royal Society grant in Newton Institute, Cambridge, UK.
• (2004) Medal "The excellent teacher" of national education of Uzbekistan.
• (2004-2005) CNR-Fellowship grant received from the Italian Center of National Researches,(6
• months duration).
• (2005-2010) Junior Associate of ICTP, Trieste, Italy.
• (2007-2012) TWAS young Affiliate, Trieste,Italy.
• (2009) Prize of TWAS for young scientists.
• (2010) TUBITAK grant, Zirve university, Turkey (1 month duration).
• (2010-2012) TWAS Research Grant (1.5 years duration).
• (2010, 2011, 2012, 2013, 2016,2017) Visiting professor fellowships, University Santiago de
• Compostela, Spain (2, 3, 1, 1, 2 and 2 months durations).
• (2011, 2013) Visiting professor fellowship, Universite du Sud Toulon Var and Centre de
• Physique Theorique, Marseille, France (1 month duration each).
• (2011) DFG AL 214/36-1 grant, Germany (1 year duration).
• (2012) TWAS young Alumnus, Trieste, Italy.
• (2012) CNRS fellowship, Centre de Physique Theorique, Marseille, France (3 months duration).
• (2013,2014) Visiting professor fellowships, Ruhr University, Bochum, Germany (2 months
• duration each).
• (2014) Grantee for ICM-2014, Seoul, Korea.
• (2014) Visiting professor fellowship, University Paris-Est, Paris, France (1 month duration).
• (2015) Resident of Aix-Marseille University, Institute for Advanced Study IMéRA, Marseille,
• France (5 months duration).
• (2016) London Mathematical Society, Scheme 2 grant, UK (2 weeks duration).
• (2016) A visiting research grant from the School of Mathematics at Leeds, UK (2 weeks
• duration).
• (2016) A visiting fellowship of University of Geneva, Switzerland (2 weeks duration).
• (2017) A State Prize from the government of Uzbekistan.
• (2017) Springer Nature TOP Author Award for high publication activity in scientific
• journals, published by Springer Nature.
• (2017) A visiting fellowship of University of Granada, Spain (1 month duration).

Selected publications

A. Book:

1.    Rozikov U.A. Gibbs Measures on Cayley Trees. World Scientific, Singapore, 2013. xviii+385 pp.   ISBN: 978-981-4513-37-1

B. Selected peer-reviewed papers in international journals (chosen among 140 papers published in international journals):

1.     Rozikov, U.A. and Sattarov, I.A. p-adic dynamical systems of (2; 2)-rational functions with unique fixed point. Chaos, Solitons and Fractals, 105 (2017), 260–270.  (doi:10.1016/j.chaos.2017.11.002).

2.     Rakhmatullaev, M.M. and Rozikov, U.A. Ising model on Cayley trees: a new class of Gibbs measures and their comparison with known ones. Journal of Statistical Mechanics: Theory and Experiment (2017), 093205 (doi:10.1088/1742-5468/aa85c2)

3.     Rozikov, U.A. Tree-hierarchy of DNA and distribution of Holliday junctions. Journal of Mathematical Biology, 75 (2017), 1715–1733 (doi:10.1007/s00285-017-1136-3).

4.    Gandolfo, D., Rahmatullaev, M.M. and Rozikov, U.A. Boundary conditions for translation-invariant Gibbs measures of the Potts model on Cayley trees. Journal of Statistical Physics, 167 (2017), 1164–1179. (doi:10.1007/s10955-017-1771-5).

5.    Kuelske C., Rozikov U.A., Fuzzy transformations and extremality of Gibbs measures for the Potts model on a Cayley tree. Random Structures and Algorithms. 50(4) (2017), 636-678.  DOI 10.1002/rsa.20671.

6.    Dzhumadil'daev A., Omirov B.A., Rozikov U.A. Constrained evolution algebras and dynamical systems of a bisexual population. Linear Algebra Appl. 2016. V.496, p. 351-380. https://dx.doi.org/10.1016/j.laa.2016.01.048

7.     Rozikov U.A., Khakimov R.M. Gibbs measures for the fertile three-state hard-core models on a Cayley tree. Queueing Syst., 81 (2015), 49–69.  doi:10.1007/s11134-015-9450-1

8.     Kuelske C., Rozikov U.A. Extremality of translation-invariant phases for a three-state SOS-model on the binary tree. J. Stat. Phys. 160 (2015), 659–680. doi:10.1007/s10955-015-1279-9

9.     Rozikov U.A., Haydarov F.H. Periodic Gibbs measures for models with uncountable set of spin values on a Cayley tree. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 18 (2015), no. 1, 1550006 (22 pages). DOI:10.1142/S021902571550006X

10.  Omirov B.A., Rozikov U.A., Tulenbayev K.M. On real chains of evolution algebras. Linear & Multilinear Algebra 63 (2015), 586–600.  doi:10.1080/03081087.2014.889131

11.  Dzhumadil’daev A., Omirov B.A., Rozikov U.A. On a class of evolution algebras of “chicken” population. Internat. J. Math. 25 (2014), no. 8, 1450073-92. doi:10.1142/S0129167X14500736

12.  Rozikov U.A., Akin H., Uguz S. Exact solution of a generalized ANNNI model on a Cayley tree. Math. Phys. Anal. Geom. 17 (2014), 103–114. doi:10.1007/s11040-014-9144-7

13.  Labra, A., Ladra, M. and Rozikov, U.A. An evolution algebra in population genetics. Linear Algebra and its Applications, 457 (2014), 348–362 (doi:10.1016/j.laa.2014.05.036).

14.  Kuelske C., Rozikov U.A., Khakimov R.M. Description of the translation invariant splitting Gibbs measures for the Potts model on a Cayley tree. Jour. Stat. Phys. 156(1) (2014) 189-200. DOI 10.1007/s10955-014-0986-y

15.  Cassandro M., Merola T., Picco P., Rozikov U.A. One-dimensional Ising models with long range interactions: Cluster expansion, Phase-separating point. Commun.Math. Phys. 327(3) (2014)  951-991. (DOI) 10.1007/s00220-014-1957-5

References

• Utkir Rozikov's CV that verifies biography, research interests, publications (includes a list.)

External links

• Utkir Rozikov at Google Scholar
• Utkir Rozikov at ResearchGate
• Utkir Rozikov at Math-Net
• Utkir Rozikov at MathSciNet

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