# International Center for Mathematical Modeling

ICMM is a centre for research in mathematical modelling, applicable within a number of different subjects and fields. Since 2000, the research group has arranged some twenty internationally renowned conferences within quantum theory (information, probability and foundations) and mathematical modeling of classical waves.

The reserch at the Department of Mathematics is organized in the research group ICMM, which is short for the International Center for Mathematical Modeling in Physics, Engineering, Economics, and Cognitive Science. Director of the center is Professor Andrei Khrennikov, who arranges its activities in cooperation with the board of ICMM.

### Main activities of the ICMM

- International projects on mathematical modeling in natural and social sciences
- Organization of international workshops and conferences
- PhD education with international base

### Main directions of investigations of the ICMM

- Mathematical methods of quantum physics, quantum probability and quantum information
- Mathematical modeling of waves and signals
- Harmonic and wavelet analysis on locally compact groups
- Stochastic analysis and financial mathematics
- Statistics and insurance
- Dynamical systems,
*p*-adic and more general algebraic dynamics *p*-adic models in cryptography and cloud computations- Mathematical modeling in biology (population dynamics, genetic code, molecular machines)
- Applications of the mathematical formalism of quantum mechanics outside of physics, decision making, cognition, psychology, economics and finances, molecular biology, genetics and epigenetics

## Our research

We consider the mathematical modeling not as just the performance of numerical calculations for some physical, technical or biological problems, but as the creation of new mathematical models to provide the adequate description of natural and social phenomena, and as the investigation of these models by using modern mathematical tools combined with advanced methods of the corresponding natural or social science.

Our main aim is to realize "multi-dimensional projects" on the boundary between a few domains of science (for instance, quantum physics + dynamical systems + information theory + neurophysiology + psychology).

These are some of our on-going research projects:

**Modeling of stochastic phenomena and financial mathematics**Astrid Hilbert, Roger Pettersson and Master and PhD students**Modeling of electromagnetic and acoustic wave phenomena**

Börje Nilsson, Sven Nordebo and Master and PhD students*p*-adic analysis, dynamical systems with applications to physics, cognitive modeling, and cryptography

Andrei Khrennikov, Ekaterina Yurova and Guiseppe Iurato**Number theory, dynamical systems, cryptography**

Andrei Khrennikov, Karl-Olof Lindahl, Marcus Nilsson, Per-Anders Svensson and Master students**Quantum foundations and quantum information**

Andrei Khrennikov and Irina Basieva**Harmonic analysis, microlocal analysis, pseudo-differential operators and applications**

Joachim Toft, Patrik Wahlberg and Master and PhD students**Complex analysis and convex optimization for EM design**

Mats Gustafsson, Sven Nordebo and Master and PhD students**Dynamical systems and biology**

Andrei Khrennikov and Torsten Lindström**Applications of quantum information for cognition and decision making**Andrei Khrennikov and Irina Basieva

## Our staff

### At Linnaeus University

- Astrid Hilbert Associate Professor
- +46 470 70 81 12
- astridhilbertlnuse

- Andrei Khrennikov Professor, Subject Representative
- +46 470 70 87 90
- andreikhrennikovlnuse

- Karl-Olof Lindahl Associate Professor
- +46 470 70 80 27
- karl-oloflindahllnuse

- Torsten Lindström Professor
- +46 470 70 81 74
- torstenlindstromlnuse

- Börje Nilsson Professor
- +46 70 304 03 77
- +46 70 304 03 77
- borjenilssonlnuse

- Marcus Nilsson Senior Lecturer, Head of Department
- +46 470 70 81 15
- marcusnilssonlnuse

- Sven Nordebo Professor
- +46 470 70 81 93
- svennordebolnuse

- Roger Pettersson Associate Professor
- +46 470 70 86 55
- rogerpetterssonlnuse

- Per Anders Svensson Senior lecturer
- +46 470 70 81 14
- per-anderssvenssonlnuse

- Joachim Toft Professor
- +46 470 70 84 65
- joachimtoftlnuse

- Patrik Wahlberg Associate Professor
- +46 470 70 86 37
- patrikwahlberglnuse

### External staff

Robert Nyqvist, Senior Lecturer, Blekinge Institute of Technology

## Board of the ICMM

**Jenny Benois-Pineau**, LaBRI, Université de Bordeaux-1/Bordeaux-2/CNRS/ENSEIRB, France,*Signal and Image Analysis***Ehtibar Dzhafarov**, Purdue University, USA,*Mathematical Psychology and Psychophysics***Christopher A Fuchs**, University of Massachusetts Boston, USA,*Quantum Foundations and Quantum Information***Mats Gustafsson**, LTH/Lund University, Sweden,*Electrical and Information Technology***Emmanuel Haven**, Institute for Quantum Social and Cognitive Science – IQSCS, University of Leicester, UK,*Econophysics and Mathematical Finances***Andrei Khrennikov**, Linnaeus University, Sweden,*Mathematical Physics, Mathematical Psychology, Dynamical Systems and Number Theory***Börje Nilsson**, Linnaeus University, Sweden,*Mathematical Modeling of Wave Phenomena***Sven Nordebo**, Linnaeus University, Sweden,*Mathematical Modeling of Wave Phenomena*

## International partners

- Institute of Applied Mathematics,
**University of Bonn**, Germany. Group of Professor S Albeverio, stochastic processes in quantum field theory. - Institute for Quantum Social and Cognitive Science (IQSCS),
**University of Leicester**, UK. Directed by Professors E Haven and S Sozzo. - Department of Psychological and Brain Sciences,
**University of Indiana**, USA. Group of Professor J Busemeyer. - Department of Informatics,
**Tokyo Science University**, Japan. Group of Professor M Ohya and N Watanabe, quantum information, non-Kolmogorov probability models. **University of Nagoya**, Japan. Group of Professor M Ozawa, quantum information.- Department of Mechanics and Mathematics,
**Moscow State University**, Russia. Group of Professor O Smolyanov, infinite dimensional analysis and quantum field theory. - Mathematical Institute,
**Russian Academy of Science**, Moscow, Russia. Group of Professor I Volovich, quantum computers and teleportation, strings, quantum field theory. - Institute of Physics,
**Serbian Academy of Sciences**, Belgrad, Serbia. Group of Professor B Dragovich, strings and gravity, feynman integration. - Faculty of Computation and Cybernetics,
**Moscow State University**, Russia. Group of Professor V Anashin,*p*-adic dynamical systems with applications to cryptography. **City University of London**, UK. Group of Professor E Pothos, quantum models of decision making.**Purdue University**, West Lafayette, USA. Groups of Professors E Dzhafarov and A Poltnitsky, quantum contextuality and quantum models of decision making, foundations of probability theory and quantum information theory.**Boston University**, USA. Group of Professor G Jaeger, quantum foundations and quantum information, foundations of probability theory.**Pavia University**, Italy. Group of Professor M D'Ariano, quantum foundations and quantum information.