User:Andrei Khrennikov, biografi

Andrei Yu.Khrennikov Андрей Юрьевич Хренников

ISSN 2070-0466, p-Adic Numbers, Ultrametric Analysis and Applications, 2018, Vol. 10, No. 4, pp. 344–347. ⃝c Pleiades Publishing, Ltd., 2018. SHORT COMMUNICATIONS Andrei Yurievich Khrennikov and his Research∗ V.S.Anashin1,2**, B.Dragovich3,4***, A.N.Kochubei5****, S. V. Kozyrev6*****, and I. V. Volovich6****** 1Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Leninskie Gory 1, 119991 Moscow, Russia 2Federal Research Center “Computer Science and Control”, Russian Academy of Sciences, Vavilov Str. 42/2, 119333 Moscow, Russia 3Institute of Physics, University of Belgrade, Pregrevica 118, Belgrade, Serbia 4Mathematical Institute, Serbian Academy of Sciences and Arts, Kneza Mihaila 36, Belgrade, Serbia 5Institute of Mathematics of the National Academy of Sciences of Ukraine, Tereshchenkivska 3, Kiev, Ukraine 6Steklov Mathematical Institute of Russian Academy of Sciences, Gubkina str. 8, Moscow 119991, Russia Received October 1, 2018 Abstract—This paper contains a brief review of a very diverse and vast scientific work of Andrei Yurievich Khrennikov on the occasion of his 60th birthday. DOI: 10.1134/S2070046618040106 Key words: Andrei Yu. Khrennikov, p-adic and ultrametric analysis, superanalysis, math- ematical models, p-adic dynamical models, probability theory, foundations of quantum mechanics, quantum-like models, p-adic modeling of cognitive and biological processes. Andrei Yurievich Khrennikov was born 1958 in Volgograd and spent his childhood in town Bratsk, in Siberia, on river Angara north from the lake Baikal. His parents were from the “romantic generation” of idealists working hardly to build a new human society. This spirit of communist romanticism filling Bratsk and other Siberian towns in 1960th played the crucial role in forming the basics of Andrei’s character. Generation-60 believed that it is possible to create totally new and unusual things. This belief was firmly incorporated in the structure of neural connections in Andrei’s brain. In the period 1975-1980 he studied at Moscow State University, Department of Mechanics and Mathematics and then in 1983 he got the PhD degree (“candidate of physical and mathematical science”) with dissertation on infinite-dimensional pseudo-differential operators from the same de- partment, under supervision of prof. Oleg Georgievich Smolyanov. In 1990 he got the second degree, “doctor of physical and mathematical science”, from the Department of mathematical physics, Steklov Mathematical Institute, Russian Academy of Sciences. This dissertation was devoted to development of the functional approach to superanalysis initiated by Profs. V. S. Vladimirov and I. V. Volovich. The main contribution was creation of the theory of generalized functions and pseudo-differential operators on superspace as well as infinite-dimensional superanalysis. The doctoral dissertation was published as Khrennikov’s monograph, Superanalysis [21], Fizmatlit (later as English translation by Kluwer). Resulting from chaos of 1990th, Fizmatlit suffered of hardfinancial problems. This book was published with the sponsorship of businessman Dmitri Aleksan- drovich Shustov. He donated 2500 USD to Fizmatlit. And at that time it was a huge amount of money. Publication of this monograph played a very important role in Khrennikov’s life and stimulated his further interest to the scientific carrier. Later Prof. A. Khrennikov continued his cooperation with Steklov Mathematical Institute by working on p-adic mathematical physics in close contact with Profs. Vasilii Vladimirov, Igor Volovich, Branko Dragovich, Irina Aref’eva, Sergei Kozyrev and Evgeny Zelenov. His main contribution to p-adics was pseudo-differential calculus for quantization of wave functions with the p-adic argument and valued in algebraic extensions of Qp as well as theory of p-adic valued probabilities. These studies were presented in the monograph, p-Adic Valued Distributions in Mathematical Physics [22]. Later this experience with the first two monographs was used for collection of research results into monographs published regularly, one per one or two years. Studies on p-adic probability stimulated Khrennikov’s interest to foundations of probability theory and, in particular, the frequency approach to probability elaborated in 1920th by von Mises. In turn probability foundations stimulated the interest to the probabilistic foundations of quantum mechanics, including such intriguing foundational problems as the probabilistic structure of the Einstein-Podolsky- Rosen argument and the Bell inequality, quantum nonlocality, and contextuality. Understanding of the crucial role of contextuality in the quantum description of observation demystifies quantum foundations. Moreover, from the contextual probabilistic viewpoint the quantum formalism can be applied not only to physical micro-systems, but also to any kind of systems sensitive to context’s variation. Corresponding mathematical models are known as quantum-like models. Nowadays they are widely used in cognition, psychology, decision making, social and political sciences, behavioral economics and finances, molecular biology, genetics, and epigenetics. Parallel to applications of quantum-like models, Prof. A. Khrennikov continued to work on applica- tions of p-adic and ultrametric analysis. In particular, he worked on theory of p-adic dynamical systems with PhD students Marcus Nilsson, Per-Anders Svensson, Robert Nyqvist, Karl-Olof Lindahl, and Ekaterina Yurova. Cooperation with Prof. Vladimir Anashin was summarized in the monograph Applied Algebraic Dynamics [9]. In Khrennikov’s research, p-adic dynamical systems served as the basis of modeling an interplay between unconscious and conscious processes in brain’s functioning and, in particular, modeling of Freud’s psychoanalysis. Cooperation with Profs. Sergey Kozyrev and Vladimir Shelkovich resulted in creation of theory of p-adic and ultrametric wavelets and pseudo-differential equations. Recently such equations started to be used in geophysics for modeling of fluids propagation, e.g., oil and water or oil-in-water emulsion, in capillary network in random porous media. This model was tested by the research team of Prof. Klaudia Olechko for real geological data collected at oil fields in Mexico. The corresponding theory of nonlinear p-adic pseudo-differential equations was developed in cooperation with Prof. Anatoly Kochubei and Aleksandra Antoniuk. Prof. A. Khrennikov started his career abroad at Bochum University and since 1997 he is professor of applied mathematics at Linnaeus University, South-East Sweden. Since 2002 he is the director of the multidisciplinary research center at this university, i.e. International Center for Mathematical Modeling in Physics, Engineering, Economics, and Cognitive Science. Research interests of Prof. A. Khrennikov can be summarized as follows: I. Mathematics, pure and applied • Infinite-Dimensional Analysis and Feynman Integration; • Functional Superanalysis; • p-Adic and non-Archimedean analysis, the Qp → Qp case; • p-Adic dynamical systems; • p-Adic and Ultrametric analysis, Wavelets, Distributions, Pseudo-Differential operators, the Qp → C case; p-ADIC NUMBERS, ULTRAMETRIC ANALYSIS AND APPLICATIONS Vol. 10 No. 4 2018

346 ANASHIN et al. • FoundationsofClassicalandQuantumprobabilitytheory. II. Physics, mathematical and theoretical • Quantization of systems with infinite number of degrees of freedom by using algebras of pseudo- differential operators on Hilbert and locally convex spaces; • Quantizationofp-adicandnon-Archimedeanphysicalsystems; • ProbabilisticfoundationsofquantummechanicsandBell’sinequality,nonlocality,andcontextu- ality; • Classical random field model of quantum mechanics. III. Mathematical Models in biology, cognition, psychology and behavioral economics, and finances, social science • Quantum-like models – molecular biology, cognition, psychology, behavioral economics and finances, social science; • Theoryofquantuminformationfieldandsociallaser; • Econophysics–modelingofpricedynamicsonthebasisofexpectationsoftradersofthefinancial market with Bohmian formalism; • Quantum-likemodelsinmolecularbiology,genetics,andepigenetics; • p-Adic dynamical models of cognitive and biological processes; • Modelinginterplayofunconsciousandconsciousinformationprocessinginthebrainwithp-adic dynamical systems; • p-Adic dynamical systems in cryptography and cloud computations. Prof. A. Khrennikov organized some 20 international conferences, particularly on foundations of quantum mechanics. He is also Deputy Editor-in-Chief of the international interdisciplinary journal “p-Adic Numbers, Ultrametric Analysis and Applications”. He is the author or coauthor of hundreds of papers. His monographs are listed in the references below [1–22]. We would like to emphasize that Prof. Andrei Yu. Khrennikov has large range of diverse research interests: from fundamental investigations to mathematical modeling and applications in various fields of sciences. He is very active, enthusiastic, energetic, creative, productive and influential scientist. He is a very kind, communicative and friendly person. At the end, we wish to Andrei Yurievich an excellent health, and to continue with his remarkable scientific activity. p-ADIC NUMBERS, ULTRAMETRIC ANALYSIS AND APPLICATIONS Vol. 10 No. 4 2018

ANDREI YURIEVICH KHRENNIKOV 347 REFERENCES 1. A. Yu. Khrennikov, S. V. Kozyrev and W. A. Zu ́ n ̃ iga-Galindo, Ultrametric Pseudodifferential Equations and Applications, Encyclopedia of Mathematics and its Applications (Cambridge Univ. Press, Cambridge, 2018). 2. E.Haven,A.KhrennikovandT.R.Robinson,QuantumMethodsinSocialScience:AFirstCourse(WSP, Singapore, 2017). 3. A.Khrennikov,ProbabilityandRandomness:QuantumVersusClassical(ImperialCollegePress,2016). 4. M. Asano, A. Khrennikov, M. Ohya, Y. Tanaka and I.Yamato, Quantum Adaptivity in Biology: from Genetics to Cognition (Springer, Heidelberg-Berlin-New York, 2015). 5. A.Khrennikov,BeyondQuantum(PanStanfordPubl.,Singapore,2014). 6. E.HavenandA.Khrennikov,QuantumSocialScience(CambridgePress,Cambridge,2013). 7. A. Khrennikov, Ubiquitous Quantum Structure: from Psychology to Finances (Springer, Berlin- Heidelberg-New York, 2010). 8. S. Albeverio, A. Khrennikov and V. Shelkovich, Theory of p-Adic Distributions: Linear and Nonlinear Models (Oxford University Press, Oxford, 2010). 9. V.AnashinandA.Khrennikov,AppliedAlgebraicDynamics(DeGruyter,Berlin,2009). 10. A.Khrennikov,InterpretationsofProbability,secondedition(DeGruyter,Berlin,2009). 11. A. Khrennikov, Contextual Approach to Quantum Formalism (Springer, Berlin-Heidelberg-New York, 2009). 12. A. Khrennikov, Introduction to Quantum Information Theory (Nauka, Fizmatlit, Moscow, 2008) [in Russian]. 13. A.KhrennikovandM.Nilsson,p-adicdeterministicandrandomdynamicalsystems(Kluwer-Springer, Dordrecht, 2004). 14. A. Khrennikov, Modeling of Processes of Thinking in p-Adic Coordinates (Nauka, Fizmatlit, Moscow, 2004) [in Russian]. 15. A. Khrennikov, Information Dynamics in Cognitive, Psychological, Social, and Anomalous Phenom- ena, Ser.: Fundamental Theories of Physics (Kluwer, Dordrecht, 2004). 16. A. Khrennikov, Non-Archimedean Analysis and its Applications (Nauka, Fizmatlit, Moscow, 2003) [in Russian]. 17. A. Khrennikov, Non-Kolmogorovian Theories of Probability and Quantum Physics (Nauka, Fizmatlit, Moscow, 2003) [in Russian]. 18. A.Khrennikov,ClassicalandQuantumMentalModelsandFreud’sTheoryofUnconsciousMind,Ser.: Mathematical Modelling in Physics, Engineering and Cognitive Sciences, 1 (Va ̈ xjo ̈ Univ. Press, Va ̈ xjo ̈, 2002). 19. A.Khrennikov,InterpretationsofProbability(VSPInt.Sci.Publishers,Utrecht/Tokyo,1999). 20. A.Khrennikov,Non-ArchimedeanAnalysis:QuantumParadoxes,DynamicalSystemsandBiological Models (Kluwer, Dordrecht, 1997). 21. A. Khrennikov, Supernalysis (Nauka, Fizmatlit, Moscow, 1997) [in Russian]. English translation (Kluwer, Dordrecht, 1999). 22. A.Khrennikov,p-AdicValuedDistributionsinMathematicalPhysics(Kluwer,Dordrecht,1994). p-ADIC NUMBERS, ULTRAMETRIC ANALYSIS AND APPLICATIONS Vol. 10 No. 4 2018