Tensor computations have garnered broad interests from pure, applied, and computational mathematics. Compared to matrix computations, tensor computations exhibit additional theoretical and practical challenges in regard to decompositions, approximations, and other problems. These challenges may be of an algebraic, analytic, numerical, or algorithmic nature. A common difficulty is the lack of tensor counterparts to classical matrix normal forms like the singular value decomposition or Jordan form. As a result, one often needs to combine tools from multiple areas such as numerical linear algebra, nonlinear optimization, computational algebra, probabilistic computation, high-dimensional approximation, etc, in order to develop efficient, provably correct algorithms for tensor computations.
This workshop aims to bring together researchers with different expertise to exchange ideas on designing computational methods for various tensor problems. One of the main features will be a focus on rigorous algorithms for which one may guarantee convergence to a global solution under reasonable conditions. Topics will include provable algorithmic guarantees in terms of computational efficiency and robustness, algorithmic techniques like spectral methods, iterative methods for nonconvex optimization, and powerful convex relaxation hierarchies like sum-of-squares, etc, where correctness guarantees may be established under suitable assumptions motivated by applications. A secondary goal is to better delineate and understand the boundary separating the possible from the impossible in tensor computations — computational tractability vs intractability, existence/uniqueness vs nonexistence/nonuniqueness of solutions, tameness vs wildness, etc.
The workshop will cover a wide range of tensor problems drawn from applications in signal and image processing, machine learning, quantum information, and scientific computing. A major impetus will be the application of tensor networks in quantum many-body physics, covering both their use in simulating physical systems and limitations imposed by quantum complexity theory.
This workshop will include a poster session; a request for posters will be sent to registered participants in advance of the workshop.
(University of Chicago)
Jiawang Nie (University of California, San Diego (UCSD))
Norbert Schuch (Max-Planck-Institut für Quantenoptik)
Anna Seigal (University of Oxford)
André Uschmajew (Max-Planck-Institut für Mathematik in den Naturwissenschaften)
Aravindan Vijayaraghavan (Northwestern University)