Speaker
Alessandro Oneto, University of Genova
Abstract
While additive decompositions and tensor rank are studied via secant varieties of Segre-Veronese varieties, Grassmannians and other classical algebraic varieties, this talk explores a different perspective: the decomposition of tensors as coefficient-wise products. I will present the general geometric framework for this approach by defining Hadamard ranks of algebraic varieties through the Hadamard products of their secant varieties. Starting from motivations coming from algebraic statistics, I will provide a general overview of the theory and discuss recent results obtained in collaboration with Dario Antolini, Edoardo Ballico, Nick Vannieuwenhoven and Guido Montúfar.