Explore the intricate connections between Liouville currents, complex structures, and Hitchin representations in this advanced mathematics lecture. Delve into key concepts such as parametrization, action of Gamma, functional representations, and the Hitchin component. Examine theorems related to symplectic manifolds, intersection currents, and closed jzuk. Investigate the Earthquake theorem and its implications for the vibration of modular space. Gain a deeper understanding of these complex mathematical topics through a comprehensive outline and in-depth analysis presented by F. Labourie.