Kieran Ryan - Maths
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I am a postdoc in mathematics at the Technical University of Vienna, in the probability group. I'm employed as part of the FWF SFB "Discrete random structures: enumeration and scaling limits".
Previously I was a postdoc at Aalto University with Eveliina Peltola, at TU Vienna with Marcin Lis, and at the University of Vienna with Alexander Glazman.
In 2021 I completed my PhD in maths at Queen Mary University of London. My supervisor was Sasha Sodin.
I work in an area of probability called statistical mechanics, which is the study of how microscopic interactions of matter induce macroscopic behaviour.
My research interests include quantum spin systems such as the Heisenberg model and XY models, 2D classical lattice models such as percolation, the six-vertex model, and dimer models, and representation theory, for example of Brauer algebras.
My papers on arXiv and Google Scholar
Preprints:
Dimerization in O(n)-invariant quantum spin chains (with Jakob Björnberg) - 2025 - [arxiv]
Publications:
Exponential decay in O(n)-invariant quantum spin systems (with Jakob Björnberg)
Annales Henri Poincaré, 2026 - [arxiv][journal]Conformally invariant boundary arcs in double dimer models (with Marcin Lis and Lucas Rey, with an appendix by Avelio Sepúlveda)
Probability Theory and Related Fields, 2026 - [arxiv][journal]Heisenberg models and Schur-Weyl Duality (with Jakob Björnberg and Hjalmar Rosengren)
Advances in Applied Mathematics Vol. 151, 2023 - [arxiv] [journal]On a class of orthogonal-invariant quantum spin systems on the complete graph
International Mathematics Research Notices, 2022 - [arxiv] [journal]The Manhattan and Lorentz Mirror Models – A result on the Cylinder with low density of mirrors
Journal of Statistical Physics, Vol. 185, No. 7, 2021 - [arxiv] [journal]
Teaching
In the summer term 2024 I taught a Master's course in Percolation at Aalto University.
Contact:
kieran[dot]ryan[at]tuwien[dot]ac[dot]at
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