I am an Associate Professor (Universitetslektor) working at Uppsala University and holder of the title of docent (Finnish: dosentti, equivalent to habilitation). I am a member of the Probability and Dynamics groups and am interested in interactions between various aspects of pure mathematics such as dimension theory, random geometry, and dynamical systems.
Previously, I was holder of the Horizons Europe Marie Skłodowska-Curie Action European Fellowship (MSCA-EF) “Dimension and Dynamics” working at the University of Oulu (Finland) and FWF Lise Meitner Senior Fellow at the University of Vienna (Austria). I was also at the University of Waterloo (Canada) for a postdoc fellowship and completed my doctorate at the University of St Andrews (Scotland) under the supervision of Kenneth Falconer and Mike Todd.
Below are the most recent pages that I added to this webpage. They may take the form of articles or news items. A full list of either can be found on the News tab.
Last week, Balázs Bárány, István Kolossváry, and I organised a focussed workshop at the Erdős Center (Rényi Institute) in Budapest. The event was centred on recent progress on self-conformal and self-similar sets, in particular analytic iterated function systems and the Fourier decay of invariant measures.
The purpose of this blog entry is two-fold:
The Department of Mathematics at Uppsala University is currently advertising several open positions.
We are looking for an Assistant Professor (Biträdande universitetslektor) in the Department of Mathematics or IT. This is a tenure-track position and an excellent opportunity for early-career researchers. More details and application instructions can be found here: Assistant Professor Position (Deadline 20 March).
We also have up to four PhD positions available in the Department of Mathematics. For more information, see: PhD Positions (Deadline 16 March). Also feel free to contact me for information if you are interested.
I am teaching the summer school course Random Geometry and Embeddability (MA3) at the 34$^{th}$ Jyväskylä summer school course. Here you can (eventually) find extra information on the course such as exercises, resources, and handwritten notes.
A few days ago, I uploaded a joint article with Balázs Bárány and Henna Koivusalo to arXiv. The article is called Dynamical covering sets in self-similar sets and I will briefly summarise the paper here.
TLDR: Imagine you are trying to cover the circle $\mathbb{S}^1$ with randomly centred balls $B(x_k,r_k)$, where $x_k$ is distributed uniformly on $\mathbb{S}^1$ and $r_k$ is a decreasing sequence. The Dvoretzky covering question1 asks for conditions on $r_k$ for the whole circle to be covered almost surely. Similarly, one can ask for when the cover is of full measure, or what size the covering set is.
In this article, we study an analogous dynamical problem for symbolic balls (cylinders) in self-similar sets, where we pick our initial point according to Bernoulli measures. We obtain a single pressure formula that describes the entire dimension theory, which shows distinct regions to the (known) homogeneous case.
The Department of Mathematics of Uppsala University is currently hiring several PhD students.
There are two open positions in the open call, see here for more information: Two PhD Positions (Deadline 31 March).
There is also an open call within the Centre of Interdisciplinary Mathematics with several more positions available: PhD Positions at CIM (Deadline 28 March).
