Hanna Oppelmayer, PhD
About myself:
I am a post-doctoral researcher in Mathematics at the University of Innsbruck, funded by the FWF ESPRIT ESP4189024 for the project "Random sub-algebras".
Research
My major interests are random walks on groups or other structures and their boundaries. Boundaries can be understood as a way of compactifying the random walks. A very powerful object in this category is the so-called Furstenberg Poisson boundary, which builds bridges between several areas of mathematics, in particular Group Theory, Probability Theory, Ergodic Theory, Dynamics and Operator Algebra Theory. One of the main tools to understand these boundaries is Entropy. In a broader frame, I investigate stationary ergodic measure spaces (non-singular actions). Boundaries are one instance of such spaces.
FWF ESP4189024: Random sub-algebras
This 3-year project aims to utilise the concept of invariant random sub-von Neumann algebras (IRA), introduced in [4]. The project has started on 3.11.2025.
Prospective researchers involved: Tattwamasi Amrutam, Yair Hartman, Tim Netzer, Ecaterina Sava-Huss
Teaching at the University of Innsbruck
- VO & PS Statistik WS 2022 and WS 2023 (Bachelor Mathematics)
- VO Stochastic 1 SoSe 2023 (Bachelor Mathematics)
- PS Stochastic 1 SoSe 2024 (teacher candidates)
- PS Linear Algebra WS 2024
Education & Employment
BSc & MSc
University of Vienna, Austria
Roland Zweimüller (master thesis advisor)
PhD
Chalmers University of Technology, Sweden
Michael Björklund
research visit
Northwestern University, USA
Yair Hartman
Post Doc
TU Graz, Austria
Wolfgang Woess
research visit
Université Paris Est Créteil, France
Sara Brofferio
Post Doc
Ben Gurion University of the Negev, Israel
Yair Hartman
Post Doc
University of Innsbruck, Austria
Ecaterina Sava-Huss
Post Doc
University of Montpellier & Sorbonne University
(employed by ANR-22-CE40-0004 GoFR)
Jérémie Brieussel & Anna Erschler
Post Doc
University of Innsbruck, Austria
(FWF ESP4189024)
Ecaterina Sava-Huss
Grants
- FWF ESPRIT 2024
- Early Stage Funding 2022
- AIANI 2022
- Knut and Alice Wallenberg Foundation: Travel Grant 2016
Publications and Preprints
[1] Boundary entropy spectra as finite subsums.
H. Oppelmayer,
Stochastics and Dynamics, Vol. 21, No. 6 (2021) 2150038, World Scientific Publishing Company,
https://www.worldscientific.com/doi/abs/10.1142/S0219493721500386
[2 ] Kudo-continuity of conditional entropies.
M. Björklund, Y. Hartman, H. Oppelmayer,
Ann. Inst. H. Poincaré Probab. Statist. 59(3): 1677-1687 (August 2023).
https://doi.org/10.1214/22-AIHP1313
[3 ] Random walks on dense subgroups of locally compact groups.
M. Björklund, Y. Hartman, H. Oppelmayer,
Trans. Amer. Math. Soc. 376 (2023), 7045-7085.
https://doi.org/10.1090/tran/8970
[4] On the amenable subalgebras of group von Neumann algebras.
T. Amrutam, Y. Hartman, H. Oppelmayer
Journal of Functional Analysis (2024) 110718.
https://doi.org/10.1016/j.jfa.2024.110718
[5] Unique ergodicity for random noninvertible maps on an interval.
S. Brofferio, H. Oppelmayer, T. Szarek
preprint (to appear in Annales de l'Institut Fourier)
https://arxiv.org/abs/2401.12361
[6] Relative stationary dynamical systems.
T. Amrutam, M. Klötzer, H. Oppelmayer
preprint
http://arxiv.org/abs/2405.17122
[7] Proximality, stability, and central limit theorem for random maps on an interval.
S. C. Hille, K. Horbacz, H. Oppelmayer, T. Szarek
preprint (to appear in Israel Journal of Mathematics)
https://arxiv.org/abs/2408.07398
[8] Unique ergodicity for noninvertible function systems on an interval.
S. C. Hille, H. Oppelmayer, T. Szarek
preprint (to appear in Studia Mathematica)
https://arxiv.org/abs/2410.18664
PhD Thesis: https://research.chalmers.se/publication/519485/file/519485_Fulltext.pdf
Master Thesis: https://utheses.univie.ac.at/detail/35394