Explore the complex world of quantum systems in this 43-minute lecture by Razvan Gurau from the University of Heidelberg. Delve into the intricacies of the Tensor Harish-Chandra–Itzykson–Zuber integral and its application in detecting entanglement in multipartite quantum systems. Presented as part of the Workshop on Noncommutative Geometry, Free Probability Theory and Random Matrix Theory at the Fields Institute, this talk offers advanced insights into the intersection of mathematical physics and quantum information theory.