Fractals in dimension theory and complex networks

Időpont: 
2019. 02. 01. 13:15
Hely: 
H406
Előadó: 
István Kolossváry (BME and Rényi)

The main aim of the Thesis is to demonstrate the diverse applicability of fractals in different areas of mathematics. Namely,
- widen the class of planar self-affine carpets for which we can calculate the different dimensions especially in the presence of overlapping cylinders,
- perform multifractal analysis for the pointwise Hölder exponent of a family of continuous parameterized fractal curves in \R^d including deRham's curve,
- show how hierarchical structure can be used to determine the asymptotic growth of the distance between two vertices and the diameter of a random graph model, which can be derived from the Apollonian circle packing problem.

I will present the results in an informal way, illustrated with plenty of examples, and some hints about the heuristics of the proofs.

Thesis advisor: Károly Simon