Tensors are the parameters used to describe multilinear maps. These data can be as simple as a multiway array of numbers, measuring information for some fixed reference frame. For a multilinear map u*v := <t|u,v> described by a tensor t, the centroid algebra of t (Cen(t)), consists of operators \sigma satisfying \sigma (u*v) = (\sigma u)*v = u * (\sigma v) is a linear invariant of t and controls its direct sum decompositions.   After introducing some linear invariants and applications, I will also ask the backwards question: given an algebra, which tensors have it as an invariant? This leads to a result relating product of algebras to products of tensors. Throughout, I will also describe recent algorithmic improvements to computing these invariants.

Refreshments will be served preceding the talk, beginning at 10:45.