Recent publications
- Tomasz Kania, Ziemowit Kostana, Discrete subgroups of normed spaces are free, Bulletin of the London Mathematical Society 57 (2025), 1650-1655
- Tomasz Kania, Natalia Maślany, Differential Embeddings into Algebras of Topological Stable Rank 1, Proceedings of the Royal Society of Edinburgh Section A: Mathematics (2024), 1-25
- Tomasz Kania, Marek Balcerzak, The existence of UFO implies projectively universal morphisms, Proceedings of the American Mathematical Society 151 (2023), 3737-3742
- Tomasz Kania, Jarosław Swaczyna, Noé de Rancourt, Continuity of coordinate functionals of filter bases in Banach spaces, Journal of Functional Analysis 284 (2023), 109869
- Tomasz Kania, Grzegorz Lewicki, A forgotten theorem of Pełczyński: (λ+)-injective spaces need not be λ-injective—the case λ∈(1,2], Studia Mathematica 268 (2023), 311-317
Interests
My research in functional analysis develops along two complementary directions. The first concerns the geometry of Banach spaces—structural and quantitative phenomena such as bases, projection properties, injectivity, and rigidity. This geometric perspective naturally extends to operators and their behaviour.
The second strand is more algebraic, focusing on Banach algebras and especially algebras of operators. I am interested in how algebraic structure interacts with operator theory and the geometry of the underlying space.
Across both areas, I draw on logic and set theory: combinatorial and foundational methods that illuminate structural questions in infinite-dimensional spaces.
More recently, I have turned to numerical methods, stochastic analysis, and applied probability, particularly in risk management, where abstract analytic structures meet quantitative modelling.
Major awards and honours
- Nagroda im. Otto Wichterle, 2021, Czeska Akademia Nauk w Pradze
Tomasz Kania
academic degree/title Doctor of Science position- Department of Functional Analysis
- Institute of Mathematics