Mark Kac Center for Complex Systems Research

Jagiellonian University


The International Ph.D. Studies in Physics of Complex Systems was created in the framework of the program announced by the Foundation for Polish Science. The aim of the project is to promote, during the next five years, fourteen Ph.D. students in the field of complex systems. To this end we have established a Consortium of five world known universities, and research laboratories, which would actively participate in educating our graduates. On a Polish side there are nine experienced scientists from the Jagiellonian University who agreed to supervise the students in their Ph. D. research and thesis preparation. Each proposed topic was consulted with the specific foreign partner who volunteered to take care of a student during his/her visit in one of the foreign institutions. In total, seventeen scientists from countries outside Poland are currently willing to participate in the program providing for our students a variety of possibilities for extended visits foreseen by the Foundation.

The subject of complex systems is a vast area of knowledge with many applications. Even though very common in everyday life, complex systems are very difficult to describe/understand theoretically. Only recently some methods are being developed to describe their behavior beginning from the first principles. All these techniques are rooted in Quantum Field Theory (QFT) - a very specialized branch of theoretical physics which was discovered more than half a century ago and is being successfully applied to describe the world of elementary particles. In short: QFT is capable to deal with quantum systems with an infinite number of degrees of freedom in general - not necessarily in the realm of elementary particle physics.

Realization of this last fact has led recently to application of field theoretical methods to statistical systems, phenomena in solid state physics, chemistry, biology, material science, physics of brain and cognitive sciences, quantum computation and quantum information - to name only few examples. Second, important factor which triggered a big progress in understanding complex systems is a dramatic increase of computing power: speed, storage and, last but not least, a development of new algorithms.