Speaker: Michał Lipiński (ISTA)
Time: 2025-11-26 16:30-17:30
Location: 1710, SIMIS
Zoom Meeting ID: 835 5518 3542 Passcode: SIMIS
摘要：
In recent years, combinatorial dynamics have become an important subject of interest due to their potential in computational methods. Forman’s (1998) theory of combinatorial vector fields has became a cornerstone of combinatorial models for continuous-time dynamical systems. About a decade ago, Mrozek (2017) extended Forman’s idea by proposing a more flexible theory of multivector fields for Lefschetz complexes, which was later generalized to finite topological spaces (Lipiński, Kubica, Mrozek, Wanner, 2022). Additionally, the Conley index theory has been adapted to the multivector fields setting, enabling a comprehensive study of combinatorial dynamical systems.
The talk will provide an accessible overview of multivector fields theory suitable for a general mathematical audience. The main definitions will be accompanied with simple examples. I will also discuss applications (e.g. in computer assisted proofs) and further developments based on the theory.
Talk mainly based on:
https://link.springer.com/article/10.1007/s41468-022-00102-9
About Speaker:
Dr. Michał Lipiński is an IST-Bridge and a Marie Skłodowska-Curie fellow at ISTA, working at the group of Herbert Edelsbrunner. Previously, he was a Postdoctoral researcher at the IMPAN, where he worked on Topological Data Analysis. He completed his PhD in Computer Science at the Jagiellonian University, under the supervision of Professor Marian Mrozek and Professor Mateusz Juda. Dr. Lipiński’s interests include, among others, Dynamical Systems, Topological Data Analysis, and Algebraic Topology. In particular, he is an expert on the application of computational topology to study Dynamical Systems.
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