Homepage of Orgoványi Vilma
About
I am a PreDoc at the HUN-REN Alfréd Rényi Institute of Mathematics. Before that I was a Ph.D. student at BME (Budapest University of Technology and Economics).
My supervior was Károly Simon.
My main interest is in random fractals which are at the cross roads of fractal geometry and stochastic processes. I study the geometric measure-theoretic properties of overlapping random self-similar sets, investigating aspects such as Hausdorff dimension, Lebesgue measure, and the existence of interior points. This work relies primarily on tools from large deviation theory and branching processes, as well as matrix product theory.
My CV.
Writings
Publications
- Projections of the random Menger sponge (with Károly Simon)
- Multitype branching processes in random environments with not strictly positive expectation matrices (with Károly Simon)
- Interior points and Lebesgue measure of overlapping Mandelbrot percolation sets (with Károly Simon)
- Stochastic Processes and their Applications (to appear)
- pdf & arXiv
- The Mathematica code used in the paper can be downloaded from here
- On the uniformity and size of microsets (with Richárd Balka and Alex Rutar)
- Mandelbrot percolation and some of its generalizations: A survey. (with Károly Simon)
- Two-scale branching functions and inhomogeneous attractors (with Alex Rutar)
PhD Thesis, and additional files
Talks & Posters & Conferences
Seminar talks
- April 2026, Positivity of Lebesgue measure of some statistically self-similar sets (long), Positivity of Lebesgue measure of some statistically self-similar sets (short)
- March 2026, home defense presentation, summarizing my PhD thesis.
- Feb 2026, Oulu Analysis Seminar, Dimensions of some statistically self-similar sets
- Jan 2026, BME Fractal Geometry Seminar, Two-scale branching functions and inhomogeneous attractors
- Nov 2024, Focused workshop on Harmonic analysis methods in fractal geometry, A few short and very introductory talks about harmonic analysis methods in fractal geometry (together with Alex Rutar)
- April 2024, St Andrews Analysis Seminar, The Lebesgue measure of some random self-similar sets
- March 2023, One Word Fractals (online), Overlapping random self-similar sets on the line (Slides)
- March 2023, Oulu Analysis Seminar (University of Oulu), Special family of random self-similar sets on the line
- September 2022, BudWiSer (Budapest University of Technology and Economics), Orthogonal projections of the random Menger sponge (Slides)
- June 2022, DAGGER (University of Warwick), Orthogonal projections of the random Menger sponge (Slides)
Conferences, Workshops, Schools
- June 2026, Fractals and Related Fields 5, Properties of some random self-similar sets with overlaps (Poster, Lightning Talk)
- September 2024, Workshop on the Geometry of Deterministic and Random Fractals II (Erdős Center)
- August 2024, School on Dimension Theory of Fractals (Erdős Center)
- June 2024, Geometry and Fractals under the Midnight Sun Conference, Properties of some random self-similar sets with overlaps (Poster, Lightning Talk)
- July 2023, Fractal geometry (ICMS)
- May 2023, Thermodynamic Formalism: Non-additive Aspects and Related Topics, Random self-similar sets on the line (Slides)
- August 2022, On geometric complexity of Julia sets - IV (Bedlewo)
- June 2022, Geometry of Deterministic and Random Fractals (BME)
- May 2022, Workshop on affine and overlapping iterated function systems (University of Bristol), Projections of the random Menger sponge (Slides, Poster)
Tanítás
A korábbi félévek anyagai itt találhatók. 2025 Stochastic processes 1 and 2025 Stochastic processes 2Contact
- e-mail: orgovanyi (dot) vilma (at) gmail (dot) com
- address: HUN-REN Alfréd Rényi Institute of Mathematics Reáltanoda utca 13-15, H-1053, Budapest, Room 307