Topological Invariants in Fixed Point Theory and Dynamical Systems

Conference and Workshop

Gdańsk University of Technology, January 29–31, 2024

Aims and Scope
The conference on Topological Invariants in Fixed Point Theory and Dynamical Systems aims to bring together researchers interested in exploring and discussing recent advances, challenges and applications of topological invariants in the realms of fixed point theory and dynamical systems. The conference provides a platform for the exchange of ideas, collaboration, and dissemination of cutting-edge research in these interconnected fields.

The key topics of the conference include:

  • Topological invariants in fixed and periodic point theory: Nielsen number, Lefschetz number, Fixed point index, Conley index,
  • Analysis of topological structures underlying dynamical systems,
  • Examination of invariant sets, attractors, and chaotic behavior from a topological perspective,
  • Computational techniques for extracting and analyzing topological invariants in fixed point theory and dynamical systems,
  • Connections between topological invariants, fixed point theory, dynamical systems and other branches of mathematics,
  • Applications in real-world problems, emerging trends and open problems in the field.

Organizing Committee
Grzegorz Graff, Paweł Pilarczyk, Justyna Signerska-Rynkowska

Important Dates
Tuesday, December 5, 2023 (extended to December 12, 2023) — registration to be completed by means of sending an email to Paweł Pilarczyk at Gdańsk Tech in order to confirm participation
Friday, January 12, 2024 — talk abstracts to be submitted by email to Paweł Pilarczyk at Gdańsk Tech (see the template below)

All the speakers are invited to send a PDF and/or LaTeX file with an abstract of their talk to Paweł Pilarczyk at Gdańsk Tech. It is suggested to use the following template: TopInv2024_Template.tex (replace "Template" in the file name with your name).

Note: Since there is no conference fee, the cost of coffee, snacks and lunches is not covered by the organizers.

Confirmed participants:

  1. Piotr Bartłomiejczyk (Gdańsk University of Technology)
  2. Michał Bogdan (Polish Academy of Sciences)
  3. Paweł Dłotko (Dioscuri Centre for Topological Data Analysis)
  4. Haibao Duan (Chinese Academy of Sciences)
  5. Grzegorz Gabor (Nicolaus Copernicus University in Toruń)
  6. Grzegorz Graff (Gdańsk University of Technology)
  7. Jacek Gulgowski (University of Gdańsk)
  8. Tomasz Gzella (Gdańsk University of Technology)
  9. Niklas Hellmer (Dioscuri Centre for Topological Data Analysis)
  10. Jerzy Jezierski (Warsaw University of Life Sciences)
  11. Frank Llovera (Gdańsk University of Technology)
  12. Łukasz Michalak (Institute of Mathematics, Physics and Mechanics, Ljubljana; Adam Mickiewicz University)
  13. Piotr Nowak-Przygodzki (Sopot)
  14. Michał Palczewski (Gdańsk University of Technology)
  15. Paweł Pilarczyk (Gdańsk University of Technology)
  16. Mateusz Przybylski (Jagiellonian University)
  17. Justyna Signerska-Rynkowska (Gdańsk University of Technology; Dioscuri Centre for Topological Data Analysis)
  18. Christopher Staecker (Fairfield University)
  19. Błażej Szepietowski (University of Gdańsk)
  20. Adam Śpiewak (Polish Academy of Sciences)
  21. Katarzyna Tessmer (Gdańsk University of Technology)
  22. Patryk Topór (Gdańsk University of Technology)
  23. Maciej Torhan (Gdańsk)
  24. Qiang Zhang (Xi’an Jiaotong University)
  25. Xuezhi Zhao (Capital Normal University)
  26. Alan Żeromski (Gdańsk University of Technology)

All the talks and discussions (except on Tuesday in the afternoon) will take place at Gdańsk University of Technology in the Faculty Council room no. 2/07 in the Nanotechnology Center, building no. 4 on the Campus Map.

The meeting begins on Monday, January 29, 2024 at 9:15am, and ends on Wednesday, January 31, 2024 at 2pm (14:00).
The lengths of talks varies between 20 and 30 minutes, including discussion.

Day One, Monday, January 29, 2024

9:15 – Opening
9:30–10:00 – Haibao Duan (Chinese Academy of Sciences): On the twisted products of spheres that have the fixed point property [Abstract PDF]
10:00–10:30 – Jerzy Jezierski (Warsaw University of Life Sciences): Nielsen number for finite abelian groups [Abstract PDF]
10:30–11:15 – Coffee break
11:15–11:35 – Patryk Topór (Gdańsk University of Technology): The indices of a fixed point under iteration of an orientation-reversing ℝ³ homeomorphism [Abstract PDF]
11:35–11:55 – Alan Żeromski (Gdańsk University of Technology): Fixed point index for boundary-preserving maps [Abstract PDF]
11:55–12:25 – Mateusz Przybylski (Jagiellonian University): The Szymczak functor on the category of finite relations [Abstract PDF]
12:30–14:00 – Lunch
14:00–14:30 – Qiang Zhang (Xi’an Jiaotong University): Some progress on fixed subgroups and fixed points [Abstract PDF]
14:30–15:00 – Xuezhi Zhao (Capital Normal University): The minimal intersection numbers of loops on surfaces [Abstract PDF]
15:00–15:30 – Michał Bogdan (Polish Academy of Sciences): Discreteness, stochasticity, geometry, topology and mechanical energy in small soft granular structures [Abstract PDF]

Day Two, Tuesday, January 30, 2024

9:30–10:00 – Paweł Dłotko (Dioscuri Centre for Topological Data Analysis): Topology and data [Abstract PDF]
10:00–10:30 – Adam Śpiewak (Polish Academy of Sciences): Predicting dynamical systems from embeddings with self-intersections [Abstract PDF]
10:30–11:15 – Coffee break
11:15–11:35 – Niklas Hellmer (Dioscuri Centre for Topological Data Analysis): From recurrence plots to random geometric complexes: Using topological data analysis for statistical hypothesis testing, with applications to detection of periodic impulses [Abstract PDF]
11:35–11:55 – Michał Palczewski (Gdańsk University of Technology): The Lyapunov exponent and rigorous computation of expansion in one-dimensional dynamics [Abstract PDF]
11:55–12:15 – Katarzyna Tessmer (Gdańsk University of Technology): Entropy-based methods in the analysis of long-term ECG recordings [Abstract PDF]
12:15–12:35 – Frank Llovera (Gdańsk University of Technology): Analysis of dynamics of a map-based neuron model via Lorenz maps [Abstract PDF]
12:40–14:00 – Lunch
Note: Afternoon session in room 121, Main Building / Gmach Główny: building no. 1 on the Campus Map:
14:00–14:30 – Błażej Szepietowski (University of Gdańsk): Geometric representations of the braid group on a nonorientable surface [Abstract PDF] (room 121, Main Building)
14:30–15:30 – Open problems session (room 121, Main Building)
19:00 – Conference dinner: Restaurant "Nowosopocka", ul. Emilii Plater 7/9/11, Sopot

Day Three, Wednesday, January 31, 2024

9:30–10:00 – Grzegorz Gabor (Nicolaus Copernicus University in Toruń): On two-point BVPs in billiard spaces [Abstract PDF]
10:00–10:30 – Christopher Staecker (Fairfield University): Thoughts on configurations of at most n points [Abstract PDF]
10:30–11:15 – Coffee break
11:15–11:45 – Łukasz Michalak (Institute of Mathematics, Physics and Mechanics, Ljubljana; Adam Mickiewicz University): Algebraic periods of surface homeomorphisms [Abstract PDF]
11:45–12:15 – Piotr Bartłomiejczyk (Gdańsk University of Technology): Expanding Lorenz maps with slope greater than or equal to √2 are leo [Abstract PDF]
12:30–14:00 – Lunch

[TopInv program PDF] – the original program of the conference in a single-page PDF file