# The 7th edition of “The International Banach Prize” has been adjudicated

9 June 2015

**Joonas Ilmavirta from Finland has been announced as the winner of the seventh edition of “The International Stefan Banach Prize for a Doctoral Dissertation in the Mathematical Sciences”. His award-winning doctoral dissertation titled “ON THE BROKEN RAY TRANSFORM”, was written under the supervision of Professor Mikko Salo at the University of Jyväskylä, Department of Mathematics and Statistics in Finland.**

In the 7th edition of the International Stefan Banach Prize for a Doctoral Dissertation in the Mathematical Sciences, the jury compared 15 doctoral dissertations: 5 from Poland, 4 from Sweden, 2 from Ukraine, and one from Finland, Hungary, Norway, Slovakia.

Already at this stage, the choice was very difficult because all dissertations were at a very high scientific level. After the first round of discussion, in a secret ballot, the jury nominated for the award the following candidates:

**Joonas Ilmavirta**(University of Jyvaskyla, Finland) dissertation title: On the broken ray transform**Michał Skrzypczak**(University of Warsaw) dissertation title: Descriptive set theoretic methods in automata theory**Martin Strömqvist**(KTH Royal Institute of Technology, Sweden) dissertation title: Homogenization in perforated domains**Błażej Wróbel**(University of Wroclaw) dissertation title: Multivariate spectral multipliers

Then, the jury again analyzed and compared in detail each of these four doctoral dissertations. Finally, as a result of subsequent ballot, the jury selected Joonas Ilmavirta as a winner.

A classical problem in X-ray computer tomography is to reconstruct a function from its integrals (averaged values) on all straight lines. This problem is extensively studied because it has several important applications in medical diagnostics. When we replace the lines with broken rays which reflect on some subset of the boundary of the domain of interest, the problem becomes much more difficult.

Dr Ilmavirta develops in his doctoral dissertation mathematical tools useful for studying this type of broken X-rays. He studies properties of the integral transform corresponding to broken ray tomography which is called the broken ray transform.

This work leads to a better interpretation of radiographs as well as to interesting and important mathematical problems, e.g. to optimization methods on Riemannian manifolds.

The jury decided to distinguish this dissertation because it is based on a difficult and interesting mathematics which leads to other interesting problems, the results have important applications in tomography, and the dissertation is very well and clearly written.

The award ceremony will take place in Warsaw during the 6th Forum of Polish Mathematicians, 8-11 September 2015. The prizewinner will receive 25 thousand PLN, the highest Prize in the competition’s history.