Natalia Maślany

PhD in Mathematics

2021–Present

Jagiellonian University
Doctoral School of Exact and Natural Sciences

Dissertation Title: Combinatorial Banach spaces and related topics: algebraic structure and self-isometries

MSc in Computational Mathematics

2019–2021

AGH University of Science and Technology
Faculty of Applied Mathematics

Thesis title: The problem of the existence of solutions for nonlinear equations in Hilbert spaces

In my thesis I research, using monotone and variational methods, solutions of nonlinear potential and non-potential equations Ax = F, where A is a strongly monotone and radially continuous operator,
and F is linear and continuous functional.

Bachelor’s degree in Mathematics

2017–2019

AGH University of Science and Technology
Faculty of Applied Mathematics

Thesis title: Naimark dilation theorem for frames

My BA thesis is devoted to the application of Naimark’s theorem
to different kinds of systems of vectors in an infinitely dimensional Banach space. In my thesis I show how in a Hilbert space extend
a Parseval frame to an orthonormal basis in a larger space and a frame to the Riesz basis. Moreover, I present the dilatation of the representation system to the Schauder basis in the Banach space.

06.06.2023

Isometries of combinatorial Tsirelson spaces , Proc. Amer. Math. Soc. 151 (2023), pp. 4475-4484 ( arXiv version )

02.05.2023

On isometries and Tingley's problem for the spaces \(T[\theta, \mathcal{S}_{\alpha}],\)
\(1 \leqslant \alpha < \omega_{1}\) , Studia Mathematica 273 (2023), pp. 285-299
( arXiv version )

20.11.2024

Differential embeddings into algebras of topological stable rank 1 Proceedings of the Royal Society of Edinburgh Section A: Mathematics (2024), pp. 1-25 ( arXiv version )
with dr hab. Tomasz Kania, prof. UJ

06.2024–12.2024

Complexity and describability in Analysis: from freeness to polishness,
SONATA BIS 13, project number 2023/50/E/ST1/00067,
(PI: dr hab. Tomasz Kania)

10.2021–12.2022

Banach spaces of continuous and Lipschitz functions
GAČR grant GF20-22230L (PI: prof. dr hab. Wiesław Kubiś)

03.2024

Receiving the Michał Jakub Łysek Scholarship for the best young mathematician at the Jagiellonian University.

01.2023 - 09.2023

Receiving a scholarship at the Doctoral School of Exact
and Natural Sciences of the Jagiellonian University
for scientifically outstanding doctoral students.

08.2022 and 12.2022

Obtaining funding for the purchase of books in the scope Research Support Module (in the first and second editions).

16.08.2024

IWOTA 2024, Canterbury

On isometries and Tingley’s problem for combinatorial Tsirelson spaces

13.06.2024

Perspektywy Women in Tech Summit 2024, Warsaw

Why do LLMs understand us?
Learn embedding techniques and create a RAG system.

18.09.2023

Developments in Modern Mathematics: a WiMGo conference, Göttingen

Differential embeddings into algebras of topological stable rank 1

07.08.2023

YMC*A 2023, Leuven

Differential embeddings into algebras of topological stable rank 1

05.10.2022

External meeting of the IM CAS, Pec pod Sněžkou

Isometries of combinatorial Tsirelson spaces

07.09.2022

IWOTA 2022, Cracow

Isometries of combinatorial Tsirelson spaces

08.2023

Linear and non-linear analysis in Banach spaces.
Lluís Santaló School 2023,
Santander

03.2023

Stochastic differential equations with R school,
Division of Statistics and Machine Learning,
Linköping University, Sweden

11.2022

Elements, Student conference on the probability, statistics,
machine learning and data analysis, AGH, Cracow

09.2022

The 9th Heidelberg Laurate Forum 2022, Heidelberg

10.2021

Workshop on Generic Structures, IM CAS, Prague

09.2021

Baby Steps Beyond the Horizon: Mathematics
for Students organized by the Mathematical Institute
of the Polish Academy of Sciences and the University
of Wrocław

03.2019

Participation in the Student Conference on Applied
Mathematics of DwuMIan organized by the Faculty
of MIM UW and the Faculty of MiNI WUT

28.11.2023

Functional Analysis, Jagiellonian University

Positive definite kernels and Hilbert C*-modules

21.11.2023

Functional Analysis, IM PAN

Differential embeddings into algebras of topological
stable rank 1

19.04.2023

Geometry of Banach Spaces, Jagiellonian University

Differential embeddings into algebras of topological
stable rank 1

07.12.2022

Geometry of Banach Spaces, Jagiellonian University

Isometries of combinatorial Tsirelson spaces

21.11.2022

Real Analysis, Lodz University of Technology

Openness of multiplication in smooth Banach *-algebras

15.11.2022

Functional Analysis, Jagiellonian University

Isometries of combinatorial Tsirelson spaces

20.04.2022

Geometry of Banach Spaces, Jagiellonian University

Lipschitz algebras and Lipschitz-free spaces
over unbounded metric spaces

12.2020

Functional Analysis, Jagiellonian University

Naimark dilation theorem

2024-2025

Computational Mathematics

UJK, Department of Mathematics, Mathematics, Bachelor’s degree,
Lecture, 30 hours

2024-2025

Computational Mathematics

UJK, Department of Mathematics, Mathematics, Bachelor’s degree,
Class, 60 hours

2024-2025

Mathematical analysis 2

UJK, Department of Mathematics, Mathematics, Bachelor’s degree,
Class, 45 hours

2024-2025

Algebra Fundamentals

UJK, Department of Mathematics, Mathematics, Bachelor’s degree,
Lecture, 45 hours

2024-2025

Algebra Fundamentals

UJK, Department of Mathematics, Mathematics, Bachelor’s degree,
Class, 45 hours

2024-2025

Mathematical analysis 3

UJK, Department of Mathematics, Mathematics, Bachelor’s degree,
Class, 60 hours

2023-2024

Mathematical analysis 2

UJK, Department of Mathematics, Mathematics, Bachelor’s degree,
Class, 45 hours

2023-2024

Elements of Game Theory

UJK, Department of Mathematics, Mathematics, Bachelor’s degree,
Lecture, 30 hours

2023-2024

Elements of Game Theory

UJK, Department of Mathematics, Mathematics, Bachelor’s degree,
Class, 45 hours

2022–2023

Mathematical analysis 1

Jagiellonian University, Faculty of Physics, Astronomy,
and Applied Computer Science, Bachelor’s degree,
Class, 30 hours

2021–2022

Mathematical analysis 2

Jagiellonian University, Faculty of Biochemistry,
Biophysics and Biotechnology, Bachelor’s degree,
Class, 45 hours

2021–2022

Tutorial 1

Jagiellonian University, Institute of Mathematics,
Bachelor’s degree, Discussion class, 10 hours

2021–Present

The member of the HRS4R Advisory Committee at Institute
of Mathematics CAS

2020–2021

Participation in the National student and doctoral student
mobility program (MOST) at the WMiI at Jagiellonian University

2018–2019

Representing the university during the AGH UST Open Days

2017–2021

The member of the Faculty Student Electoral Commission
of the AGH University of Science and Technology in Cracow

2017–2021

The member of the Mathematics Students Association of AGH University of Science and Technology

2016–2019

Representing the University during the Friday Night
of Exact Sciences of AGH and during the Festival of Science
and Art in Cracow