Speaker: Michał Lipiński (ISTA)
Time: 2025-11-28 11:00-12:00
Location: 1710, SIMIS
Zoom Meeting ID: 884 9577 9498 Passcode: SIMIS
Abstract:
A notion of continuation of an isolated invariant set has been recently introduced in the multivector fields framework (Dey, Lipiński, Mrozek, Slechta, 2022). This allows to model and study parameterized flows in a combinatorial setting. Moreover, the combinatorial language fits naturally within the framework of persistent homology—the main workhorse of topological data analysis (TDA). In our recent work (Dey, Lipiński, Soriano-Trigueros 2025) we show how ideas from TDA can be used to characterize the evolution of a vector field, and the bifurcations it undergoes.
In this talk, I will briefly recall the main idea behind combinatorial multivector fields, persistent homology, and combinatorial continuation, and explain how these concepts can be combined together to construct the Conley-Morse persistence barcode encoding evolution of a vector field.
Talk mainly based on:
https://arxiv.org/abs/2504.17105
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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