Explore the intricacies of fusion products and finite-dimensional quotients in periodic Temperley-Lieb algebras through this 55-minute lecture by A. Morin-Duchesne from Ghent University. Delve into the realm of integrability in Condensed Matter Physics and Quantum Field Theory as part of the NCCR SwissMAP series. Gain insights into the mathematical structures and techniques used to analyze these complex algebraic systems and their applications in theoretical physics.