Francesco Galuppi

Abstract

The signature of a path is a sequence of tensors which allows to uniquely reconstruct the path. In this paper we propose a systematic study of basic properties of signature tensors, starting from their rank, symmetries and conciseness. We prove a sharp upper bound on the rank of signature tensors of piecewise linear paths. We show that there are no skew-symmetric signature tensors of order three or more, and we also prove that specific instances of partial symmetry can only happen for tensors of order three. Finally, we give a simple geometric characterization of paths whose signature tensors are not concise.

Our speaker

Francesco is Assistant professor at Warsaw University, Faculty of Mathematics, Informatics and Mechanics and is the principal investigator of the Sonata grant "Tensor rank and its applications to signature tensors of paths" project awarded by the National Science Center, Poland.  His background is in complex algebraic geometry. He likes to interact with mathematicians with different backgrounds to explore applications of his expertise.  He has a Master Degree in Mathematics from the University of Padova and a PhD in Algebraic Geometry.

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