Multipartite entanglement is a crucial resource for quantum communication and computation, enabling exciting applications of quantum information science such as efficient algorithms to factor large integers or simulate complex physical systems. However, the exponential scaling of the dimension of multipartite quantum systems and the presence of environmental noise make a precise mathematical characterization of entanglement challenging. The goal of this project is to study the behavior of multipartite quantum correlations under the influence of environmental noise through the lens of symmetries. Understanding the interplay of correlations and noise is crucial to analyzing the performance of quantum communication protocols and informs the design of error-correcting codes that protect quantum information from decoherence. This project will develop versatile methods to tightly characterize the fundamental limits of faithful quantum communication and provide tools to analyze the asymptotic behavior of multipartite entanglement in large systems undergoing noisy quantum evolution. The research efforts of this project are complemented by the development of an online summer course at the undergraduate level teaching advanced concepts in linear algebra that are needed to start research in quantum information theory. The publicly available course will be specifically aimed at undergraduate students transferring from community colleges to research-active institutions and students intere