ODT - THESIS TOPIC: Balázs Bárány: Geometric properties of non-conformal ...


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Thesis topic proposal

Geometric properties of non-conformal sets

THESIS TOPIC PROPOSAL

Institute: Budapest University of Technology and Economics
mathematics and computing
Doctoral School of Mathematics and Computer Sciences

Thesis supervisor: Balázs Bárány
Location of studies (in Hungarian): Department of Stochastics
Abbreviation of location of studies: BME

Description of the research topic:

Benoit Mandelbrot described the fractal sets as "irregular and fragmented patterns around us". Such fractal sets can be constructed using iterated function systems. The main purpose of the project is to study the geometric properties of the attractors of IFSs consisting of non-conformal mappings, like Hausdorff- and Tricot-dimension and measure, the dimension of shrinking target subsets, and multifractal analysis.
The task of the PhD student is first to get a deep understanding of the existing results of the field and then make significant progress. The prospective student will be part of our very strong Dynamical Systems research group.

Required language skills: English
Further requirements:
ergodic theory, measure theory, probability 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).