Sascha Troscheit

Short Bio: I am a MSCA research fellow at the University of Oulu, and holder of the Horizons Europe Marie Sklodowska-Curie Action European Fellowship (MSCA-EF) "Dimension and Dynamics" that investigates the interplay between dimension theory, dynamical systems, embeddability, as well as probability theory. From June 2020 to August 2022, I was senior research fellow at the University of Vienna (Austria) and PI of the FWF (Austrian Research Fund) Senior Lise Meitner Research Fellowship FWF M-2813: "Regularity and embeddability of self-similar processes". I previously held positions at the University of Vienna, the University of Waterloo, the Institut Mittag-Leffler and ICERM, Brown University. I completed my doctorate at the University of St Andrews under the supervision of Kenneth Falconer and Mike Todd. In June 2023 I was awarded the title of Docent (dosentti) of the University of Oulu, an academic title which is roughly equivalent to habilitation.

Research Interests: My research focusses on random (fractal) geometry, branching processes, symbolic dynamics, dimension theory, and their interplay with number theory. I have worked with stochastic self-similarity, gauge functions for stochastic attractors, and study the fine structure of sets and measures. In particular, I have studied the Assouad dimensions of random processes and determined phase transitions on their small scale behaviour. Most recently, I have looked into the Brownian continuum tree and Brownian map and applied dimension theory to study quasi-symmetric embeddings. I am currently working on the connection between analytical properties of real-valued functions and their associated continuum trees.

One World Fractals: Together with Jonathan Fraser, Thomas Jordan, Natalia Jurga, Antti Käenmäki, and Henna Koivusalo I am organising a bimestrial hybrid seminar in fractal geometry and adjacent fields. More information can be found on its webpage: oneworldfractals.org.

Older Conferences & Workshops: To view the webpages of conferences and workshops that I have (co-)organised in the past please see the links page. It has a full listing of past events' webpages for "posterity".

Other Interests and "Fun Facts": I am an active long distance sailor (mostly single-handed) and have sailed most of the British, German, Dutch, Belgian and French Atlantic coast with several North Sea crossings. My last year of PhD was spent afloat, writing up my thesis on a sailing boat. I like tinkering with electronics, programming, and command a small army of Arduinos. My most recent "achievement" is a fully working solid-state fridge.

Other trivia. My Erdős number is 3: Troscheit— \(x\) Hare*—Shallit—Erdős (where \(x \in\{K. E., K. G.\}\)) and Troscheit—Falconer—Guy—Erdős.
My Einstein number is 5: Troscheit—Neukirch—Kiessling—Lebowitz—Bergmann—Einstein.
My Bacon number is 4: Troscheit(—*)Lustig—Brennicke—Gampu—Bacon (*uncredited extra)
And my Sabbath number is 4: S. Troscheit (me)—S. Troscheit (my father)—Roy Black—The Muppets—Black Sabbath (under a loose definition of musical collaboration)
which makes my Erdős-Bacon-Sabbath number 11.