Tensors and hypermatrices


Lek-Heng Lim
2013-01-02  10:10 - 11:00
Room 103 , Mathematics Research Center Building (ori. New Math. Bldg.)

We will discuss some exciting new developments in the studies of high-order tensors and their coordinate-dependent form, hypermatrices. We argue that a subject that parallels matrix theory and numerical linear algebra is emerging from these recent developments. Examples will be drawn from algebraic geometry (hyperdeterminants, secant varieties), biology (phylogenetic invariants), computer science (computational complexity, quantum computing), optimization (self-concordance, higher-order optimality conditions), physics (Yang-Baxter equation), signal processing (blind source separation), statistics (multivariate moments and cumulants), etc. We shall see how this subject can provide a unifying view of seemingly disparate topics.