Center for Interdisziplinary Research

p-Adic Methods for Modelling of Complex Systems

Date: April 15 - 20, 2013

Convenors: Sergio Albeverio (Bonn, GER), Igor Volovich (Moskau, RUS), Sergei Kozyrev (Moskau, RUS), Andrei Khrennikov (Växjö, SWE), Branko Dragovich (Belgrad, SRB) und Vladimir M. Shelkovich † (St. Petersburg, RUS)

The workshop on 'p-Adic Methods for Modeling of Complex Systems' discussed applications of p-adic analysis to modeling of various phenomena and comparison of these methods with established methods of analysis over real numbers.
In science, after Newton and Leibniz, it is used mathematical analysis based on real numbers. However, irrational real numbers are unobservable. In experiments one can observe only rational numbers. To do mathematical analysis one needs a completion of rationals and due to the Ostrovsky's theorem only real or p-adic number fields can be obtained.
There are applications of ultrametric methods to Planck scale physics, theory of spin glasses, biology (genetics, protein dynamics), cosmology.
These applications can be considered as an example of duality between simple and complex behavior. Simple phenomena can be modeled with the help of real models, and for modeling of complex phenomena one needs p-adic methods. p-adic methods are well suited to description of hierarchy in complex systems.
The goal of the activity presented at the Workshop is to establish p-adic and ultrametric analysis as an alternative to analysis over real numbers. Mathematical methods of ultrametric analysis are already well developed and are able to describe a wide variety of phenomena. There are well known mathematical aspects of p-adic analysis: applications to number theory, algebraic geometry, represention theory, ultrametric analysis, dynamical systems, partial differential equations, wavelets, etc. The main challenge of p-adic modeling is related to effective applications of p-adic analysis.
Already developed applications of p-adic analysis include quantum theory, strings, spin glasses, cosmology, turbulence, renormalization theory, dynamics of proteins, genetics, data mining, economics, psychology. We expect new applications of p-adic methods.

Talks given at the Workshop belong to the following directions:

To conclude, the workshop was very successful, many new important and exciting results were reported. The workshop will stimulate new progress in the field of applications of p-adic methods to modeling of complex systems.

Teilnehmerinnen und Teilnehmer

Vladimir Anashin (Moskau, RUS), Irina Ya. Aref'eva (Moskau, RUS), Ekatarina Yurova Axelsson (Växjö, SWE), Erik Makino Bakken (Trondheim, NOR), Alexander Bendikov (Wroclaw, POL), Patrick E. Bradley (Karlsruhe, GER), Bertin Diarra (Aubière, FRA), Trond Digernes (Trondheim, NOR), Alain Escassut (Aubière, FRA), Sergei Evdokimov (St. Petersburg, RUS), Alexander Grigor'yan (Bielefeld, GER), Pei-Chu Hu (Jinan, TPE), Emily King (Berlin, GER), Anatoly N. Kochubei (Kiew, UKR), Alexei Koshelev (Brüssel, BEL), Alexander Kosyak (Bonn, GER), Ligmin Liao (Créteil, FRA), Yuri Manin (Bonn, GER), Mukadas D. Missarov (Kazan, RUS), Fionn Murtagh (Egham, GBR), Enno Nagel (Maceió, BRA), Zoran Rakic (Belgrad, SRB), Oded Shor (Rehovot, ISR), Maria Skopina (St. Petersburg, RUS), Brunello Tirozzi (Rom, ITA), Sergii Torba (Mexico City, MEX), Livat Tyapaev (Saratov, RUS), Franco Vivaldi (London, GBR), Apostolos Vourdas (Bradford, GBR), Sang Tae Jeong (Incheon, KOR), Evgeny Zelenov (Moskau, RUS), Wilson A. Zúñiga-Galindo (Mexico City, MEX)

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