# Mathematics and Physics of Complex Systems.

The concept of complex system is certainly one of the most fruitful paradigms for modelling and predicting behaviour of large systems in physics, life sciences, and information technology.

A complex system is a collection of a large number of relatively simple, similar components whose individual behaviour and interactions can be described by simple laws. However from the interaction of large numbers of such elements, which is beyond any direct analytical description, emerges a collective behaviour of the whole system which can undergo phase transitions between macroscopic modes, store, process, and transmit information, and feature chaotic, unpredictable dynamics even if all its elementary components are fully deterministic.

The study of an object as rich as complex systems require combination of a diverse array of methods ranging from probabilistic and statistical to algebraic and number theoretic, as well as to methods of statistical physics and field theory.

## Topics:

- mathematical theory of information and control,
- stochastic systems with many components,
- algebraic geometry and number theory,
- combinatorial and probabilistic aspects of representation theory,
- modal logics,
- integrable systems,
- statistical and quantum field theory.