NCN project „Topological and Numerical Methods in Dynamical Systems” | Faculty of Applied Physics and Mathematics at the Gdańsk University of Technology

Page content

News

Date added: 2022-03-25

NCN project „Topological and Numerical Methods in Dynamical Systems”

NCN project „Topological and Numerical Methods in Dynamical Systems”
Since January 13, 2022, there is a new NCN-funded research project running at our Faculty. The research focuses on selected topological and numerical methods in dynamical systems.

This is a three-year-long computational mathematics project awarded to our faculty member, dr hab. Paweł Pilarczyk, in the total amount of 376,370 PLN. The project includes international academic collaboration and some scholarships for MSc or PhD students. Its description is available NCN's website: https://projekty.ncn.gov.pl/en/index.php?projekt_id=521876.

The main objective of the project is to develop some computational tools for the purpose of automated analysis of dynamics, and to apply them to certain systems. Instead of plain numerical simulations, the project aims at using rigorous numerical methods and topological tools such as the Conley index. In this way, the results obtained fall in the category of computer-assisted proofs.

Another topic to investigate is the phenomenon of chaotic itinerancy. It is the case when trajectories in a dynamical system stay for a prolonged time around certain states (quasi-attractors) and wander between these states in a chaotic manner. This phenomenon has been used by Japanese neuroscientists since the 1990s to explain brain activity, and current applications include designing spontaneous behavioral switching of robots.

Paweł Pilarczyk is a mathematician and computer scientist with extensive international experience. Before joining Gdańsk Tech in 2018, he worked at the Jagiellonian University (Kraków, Poland), Georgia Institute of Technology (Atlanta, GA, USA), Kyoto University (Japan), University of Minho in Braga (Portugal), Institute of Science and Technology (Austria), and California State University Channel Islands (USA). His publications include over 30 papers with more than 40 international co-authors, over 300 citations, Hirsch index of 10, and at least 50 talks delivered at international conferences. At Gdańsk Tech, he mainly teaches courses at the Data Analyst specialization in mathematics.

12 views