Explore a 56-minute scientific lecture examining the injective norm of random tensors and quantum states, delivered by Stéphane Dartois from Université Paris Saclay and CEA at IHES. Delve into the mathematical concept of injective norm as it extends from matrix operator norms to tensors, and discover its significance in quantum information as a measure of genuine multipartite entanglement. Learn about new research providing high-probability upper bounds on injective norms of real and complex Gaussian random tensors, which yields insights into geometric entanglement of random quantum states and ground-state energy in multispecies spherical spin glass models. Understand how the Kac-Rice formula approach improves upon previous ε-net techniques to establish tighter constant bounds in specific cases.