Title: NL bialgebras
Speaker: Zohreh Ravanpak
Institution: University of Timișoara
Date & Time: September 26, 2024, 15:30–16:30
Location: Seminar Room 5, Mathematics Building, Jilin University
In this talk, we introduce the concept of (weak) NL bialgebras, exploring Poisson-Nijenhuis structures on manifolds within the framework of Lie bialgebras. These structures shed light on the interplay between Nijenhuis operators and Lie bialgebras that satisfy specific compatibility conditions. We demonstrate how such conditions enable the construction of a hierarchy of compatible Lie bialgebras—both on the original Lie algebra and its deformed versions via the Nijenhuis structure of any order. As an application, we analyze a well-known dynamical system, a specific case of the Euler top, and show that its underlying algebraic structure is a weak NL bialgebra.
This talk is based on recent work: https://arxiv.org/pdf/2404.17708
Zohreh Ravanpak completed her PhD in 2018 in Iran, including a doctoral internship at WSMCS (Warsaw) and a six-month research stay at the University of La Laguna (ULL, Spain). She subsequently worked as a postdoctoral researcher at the Polish Academy of Sciences (Warsaw) and the Max-Planck Institute for Mathematics (Bonn). Currently, she is a young researcher at the University of Timișoara, Romania. Her research focuses on differential geometry and mathematical physics, with an emphasis on integrable systems (Hamiltonian and bi-Hamiltonian), Poisson geometry, Lie theory, and Lie groupoids.
