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Explore Floer homology with differential graded (DG) coefficients and its applications to cotangent bundles in this advanced mathematics lecture. Delve into the definition of Hamiltonian Floer homology with coefficients in a DG local system for symplectically aspherical cases. Examine how this homology fits into a filtered homological toolbox and discover various dynamical applications to cotangent bundles. Learn about the collaborative work of Alexandru Oancea, Jean-François Barraud, Mihai Damian, and Vincent Humilière, while also gaining insights into the original construction by Barraud-Cornea and subsequent developments by other mathematicians. Engage with complex concepts in symplectic geometry and topology as presented by Alexandru Oancea from the University of Strasbourg during this Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar.