Defective Tensor Network Varieties

Explore the intricacies of defective tensor network varieties in this 52-minute lecture presented by Alessandra Bernardi from the Università di Trento at IPAM's Tensor Networks Workshop. Delve into the structured world of tensor networks within algebraic varieties, examining their dependence on graph structure, bond dimensions, and physical dimensions. Investigate the expected dimensions of these varieties, primarily influenced by parameter count and gauge subgroup effects. Uncover the enigmatic realm of defective tensor networks, anomalies that defy conventional expectations and remain unclassified. Recorded on February 8, 2024, at the Institute for Pure & Applied Mathematics (IPAM) at UCLA, this talk offers a deep dive into an advanced topic in mathematical physics and tensor network theory.