Thesis supervisor: Károly Simon
Location of studies (in Hungarian): Department of Stochastics Abbreviation of location of studies: BME
Description of the research topic:
In 1970’s Mandelbrot pointed out that fractals appear everywhere. In biology, geology, physic, finance etc.. We study the geometry of fractal sets. In particular, we focus on attractors of certain dynamical systems which are called self-similar or self-conformal iterated function systems. To study this kind of fractals, one needs to have knowledge of ergodic theory and dynamical systems and also of geometric measure theory. In our
department, there is a very strong group working on dynamical systems. So, the prospective Ph.D. student will be able to obtain the required knowledge from dynamical systems on our numerous dynamical systems courses on the go. We study this self-similar sets from the point of their Hausdorff or other fractal dimensions.
In recent years there has been a very significant achievement on this field but the most important problem of the field still remain open. The task of the Ph.D. student is first to get a deep understanding of the existing results of the field and then make significant progress in this field. The prospective student will be part of our very strong Dynamical Systems research group.
Required language skills: English Further requirements: Basic knowledge of measure theory.
Number of students who can be accepted: 1
Deadline for application: 2024-05-31
2024. IV. 17. ODT ülés Az ODT következő ülésére 2024. június 14-én, pénteken 10.00 órakor kerül sor a Semmelweis Egyetem Szenátusi termében (Bp. Üllői út 26. I. emelet).
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