Tomasz Kania
Research Interests
My work lies broadly in functional analysis, exploring both geometric and algebraic aspects of the field. I focus particularly on the geometry of Banach spaces, the structure of Banach algebras, and operator theory. I am especially interested in the ideal structure of algebras of operators on classical Banach spaces and in questions concerning Grothendieck spaces and their operator-theoretic characterisations.
A distinctive feature of my research is the application of set-theoretic methods to problems in analysis, including infinitary combinatorics, elementary submodels, large cardinals, and descriptive set theory. I also maintain interests in stochastic processes and quantitative finance.
Publications
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From Instagram @mathsy_plOpen Problems
Questions I'm thinking aboutIs convolution in $\ell^1(\mathbb{Z})$ an open map?
I would like to know whether convolution is open (maps open sets to open sets) when viewed as a map $\ell_1(\mathbb{Z}) \times \ell_1(\mathbb{Z}) \to \ell_1(\mathbb{Z})$; equivalently whether multiplication in the Wiener algebra is open.
Toroidal Elton–Odell and the rephasing trap in the Ramsey reduction
I want to circumvent combinatorial obstacles for establishing a toroidal version of the Elton–Odell separation theorem for infinite-dimensional complex normed spaces.
Selected Talks & Events
Full archive →53rd Winter School in Abstract Analysis
Functional Analysis in the Pacific Northwest
XXXIX International Summer Conference on Real Functions Theory
52nd Winter School in Abstract Analysis
Analysis Seminar Innsbruck
IWOTA 2024 — 35th International Workshop on Operator Theory and its Applications
Geometry of Banach and Metric Spaces and Fixed Point Theory
Lattice Structures in Analysis and Applications
51st Winter School in Abstract Analysis
SUMIRFAS — Summer Informal Regional Functional Analysis Seminar
Concentration Week on Ideals and Algebras of Operators on Banach Spaces
WorC(K)shop
50th Winter School in Abstract Analysis
Mikrokonferencja z procesów stochastycznych
Workshop on Banach spaces and Banach lattices
49th Winter School in Abstract Analysis
48th Winter School in Abstract Analysis
Analysis Seminar Innsbruck
Workshop on Banach spaces and Banach lattices
Jubilee Congress for the 100th anniversary of the Polish Mathematical Society
Preserver Weekend in Szeged
Function Spaces XII
Geometrical Aspects of Banach Spaces
Geometric Topology and Geometry of Banach Spaces
Selected Seminar Talks
Seminar
Seminar
Functional Analysis Seminar
Real Analysis Seminar
Seminar on Geometry of Banach spaces
Analysis Seminar
Banach Spaces Webinar
Colloquium
Abstract Analysis Seminar
Operator Algebras Seminar
Seminar Talk
Analysis Seminar
Seminar Talks
Set-theory Seminar
Descriptive Set Theory Seminar
Analysis Seminar
Analysis Seminar
Teaching
All materials →Python in Finance, Finance in Python
Python is one of the most widely used object-oriented programming languages, whose popularity continues to grow thanks to Data Science libraries such as numpy, pandas, and scikit-learn. This course presents selected topics in Finance including interest rate models, option pricing (Black–Scholes, Cox–Ross–Rubinstein, and other models), derivative pricing, and simulations using binomial trees/lattices and Monte Carlo methods—all implemented in Python.
Topics include algorithmic trading, Value-at-Risk estimation, portfolio liquidity, and Big Data techniques. While emphasis is placed on programming (mainly in Jupyter notebooks), mathematical content such as properties of solutions to stochastic differential equations is treated rigorously.
I have also taught courses in Functional Analysis, Banach Spaces, and related topics. For lecture notes and additional materials, visit my teaching page.
Education
Supervisor: Tomasz Wachowicz
Supervisor: Niels J. Laustsen
Supervisor: Aleksander Błaszczyk
Past Academic Positions
PI: Professor David Preiss, FRS
Professional Service
Grant Referee
- Natural Sciences and Engineering Research Council of Canada (NSERC)
- Polish National Agency for Academic Exchange (NAWA)
- Estonian Research Council (6×)
Member of the Mathematics and Computer Science panel of the Estonian Research Council (2022–2023)
Habilitation Referee
PhD Thesis Referee
PhD Supervision
MSc Supervision
Grants and Awards
Awards
Awarded by the Czech Academy of Sciences in Prague, given to researchers under 35 years of age. Named after Otto Wichterle, one of the first members of the Czechoslovak Academy of Sciences, chemist and inventor of contact lenses. Recognised in mathematics for a series of publications on the geometry of Banach spaces, specifically qualitative and quantitative descriptions of separated sets on spheres of Banach spaces.
Grants
NCN SONATA 15
Geometria lipschitzowska przestrzeni metrycznych oraz stowarzyszona z nią teoria operatorów i analiza harmoniczna
Lipschitz geometry of metric spaces and associated operator theory and harmonic analysis
Narodowe Centrum Nauki (National Science Centre, Poland)
GAČR Project 19-07129Y
Metody lineární analýzy v operátorových algebrách a naopak
Linear-analysis techniques in operator algebras and vice versa
Postdoctoral Researchers
Doktorská škola pro vzdělávání v oblasti matematických metod a nástrojů v HPC
Doctoral School for Education in Mathematical Methods and Tools in HPC
Visiting the University of Cambridge for the purpose of transferring know-how concerning the organisation of PhD studies in High-Performance Computing. The final report serves the Czech government in the ongoing process of modernisation of programmes in the area of HPC.