On 13th September Adam Kanigowski from the Institute of Mathematics of the Polish Academy of Sciences PAN was awarded the International Stefan Banach Prize for his dissertation entitled “Ergodic properties of smoothflows on surfaces”. The award ceremony took place during the inauguration of the 7th Forum of Polish Mathematicians with the participation of Ukrainian mathematicians at the University of Warmia and Mazury in Olsztyn.
The other nominees were:
The prize-winning doctoral dissertation winning dissertation entitled “Ergodic properties of smoothflows on surfaces” was written under the supervision of professor Mariusz Lemańczyk from the Faculty of Mathematics and Computer Science of the Nicolaus Copernicus University in Toruń and the auxiliary supervisor – Dr. Joanna Kułaga-Przymus, from the Institute of Mathematics of the Polish Academy of Sciences and Faculty of Mathematics and Computer Science of the Nicolaus Copernicus University in Toruń
The theory of dynamical systems considered in the winning dissertation have been often used in biology, economy, astronomy, meteorology, hydrodynamics, and in many other fields of science. Its foundations were developed by Sir Isaac Newton, and the discovery of the chaos theory in the twentieth century helped to explain many phenomena happening both in nature and in economics. Every day we have to deal with phenomena of this type as we watch weather forecasts which, unfortunately, are never totally accurate, which is compliant with the contemporary theory of dynamical systems. The theory of dynamical systems also enables us to determinate complicated trajectories of satellites in such a way that fuel can be saved.
In the award-winning thesis, Dr. Kanigowski examines smooth dynamical systems which preserve the measure on surfaces, while he attempts to describe their ergodic properties and different types of mixing. The main issue considered in the thesis is the problem raised by W.A. Rochlin who wondered whether the usual mixing by such a dynamical system implicates the mixing of higher orders. For smooth dynamical systems, this problem has been open for 50 years. Dr. Kanigowski proposes a solution for certain classes of dynamical systems: the so-called Arnold flow and Koczergin flow.
The thesis consists of over 100 pages of difficult mathematics. It contains a well-written introduction and clearly summarizes the achieved results as well as presents them in comparison with what was achieved earlier. The winning thesis of Dr. Kanigowski constitutes the basis for his 4 publications. Three of them have already been published: one in Inventiones mathematicae (one of the most prestigious mathematics journal) and two in Ergodic Theory and Dynamical Systems (one of the most important magazines which publishes works on dynamical systems).
The International Stefan Banach Prize has been awarded annually since 2009. It is funded by Ericpol, which in 2008 together with the Polish Mathematical Society established prestigious distinction. The prize reflects a leading Polish IT company’s appreciation of mathematics and its role in the modern world. The goal of the project is to increase global awareness of the work of Stefan Banach and Polish science. It is also one of the greatest financial awards in the field of mathematics in Poland. The amount of the prize is now 25,000 PLN (20,000 PLN as of 2013). The competition now ranks as one of the most important mathematical events in Europe.