Seminars

On Tuesday March 22nd,  at 10:30 in room Byron 106

Alessandra Bernardi (GALAAD - INRIA) will speak on

Polynomial and Tensor Decompositions

---

An Algebraic Geometry problem coming from a Nomuber theory problems asked: "Which is the minimum integer $r$ that is needed to write a generic homogeneous polynomial of degree $d$ as sum of $r$ $d$-th powers  linear forms"? This problem is equivalent to the knowledge of the dimension of secant varieties of veronese varieties that was completely solved by J. Alexander A. Hirschowitz in 1995.
If we formulated the analogous problems in terms of any other kind of polynomial we get into open problems that are of great interest both from the pure and the applied mathematics.
The study of secant varieties to varieties parameterizing homogeneous polynomials had a substantial interest in the literature and has been extended to the more general study of secant varieties of varieties parameterizing tensors which are closely related to the rank of general tensors (i.e. to find the minimum number of rank one tensor that are needed to write a given generic tensor). The knowledge of the rank of a tensor, its possible decomposition in terms of tensors that have special symmetries, is currently of major interest in the field of applications such as the theory of telecommunications, medicine, phylogenetics, statistics ...