Abstract for the talk on 24.02.2017 (10:00 h)Reading Group on High Dimensional Algebraic Geometry
Mario Kummer (MPI MIS, Leipzig)
Bounded-rank tensors are defined in bounded degree
24.02.2017, 10:00 h, MPI für Mathematik in den Naturwissenschaften Leipzig, G3 10 (Hörsaal)
We will present an article by Jan Draisma and Jochen Kuttler where they prove that for each k there exists an upper bound d=d(k) such that tensors of border rank at most k are defined by the vanishing of polynomials of degree at most d, regardless of the dimension of the tensor and regardless of its sizes in each dimension. The proofs are based on the methods introduced in the previous session of the reading group: It involves passing to an infinite-dimensional limit of tensor powers of a vector space and exploiting the symmetries of this limit in a crucial way.