propose to open International Ph.D. Studies in the framework of the program
recently 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
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.
In accord with the above short characteristic of the field of complex systems, the Ph.D. topics we offer in the present program, cover a large variety of subjects. Beginning with purely theoretical problems of quantum gravity and gauge theories, via studies of subtle phenomena in solid state and quantum optic, up to problems in biology and finally to quantum computing and quantum information - a student has a large choice of interesting subjects depending on his/her interests.
To summarize: we believe that, e.g., Quantum Chromodynamics, Quantum Gravity and String Theory are essential examples of complex systems known today, and that some students will be as fascinated by them as some of us are. At the same time, due to a rapid growth of knowledge and due to vanishing boundaries between different disciplines, the methods developed to study these theories are becoming crucial for a progress in studying other bio/info/techno structures.
A short description of each topic, together with the name of the supervisor, follows below. Details of the international partners are given in the foreign partners section.