Tensors, invariants, and optimization


Walter, M. (2020). Tensors, invariants, and optimization. Perimeter Institute. https://pirsa.org/20060049


Walter, Michael. Tensors, invariants, and optimization. Perimeter Institute, Jun. 17, 2020, https://pirsa.org/20060049


          @misc{ pirsa_PIRSA:20060049,
            doi = {10.48660/20060049},
            url = {https://pirsa.org/20060049},
            author = {Walter, Michael},
            keywords = {Quantum Information},
            language = {en},
            title = {Tensors, invariants, and optimization},
            publisher = {Perimeter Institute},
            year = {2020},
            month = {jun},
            note = {PIRSA:20060049 see, \url{https://pirsa.org}}

Michael Walter University of Amsterdam


Given a vector in a representation, can it be distinguished from zero by an invariant polynomial? This classical question in invariant theory relates to a diverse set of problems in mathematics and computer science. In quantum information, it captures the quantum marginal problem and recent bounds on tensor ranks. We will see that the general question can be usefully thought of as an optimization problem and discuss how this perspective leads to efficient algorithms for solving it.