Strassen's conjecture states that computational complexity is additive when the variables are independent. For example, there is no more efficient way to multiply two pairs of matrices than multiply each pair separately.
Strassen's conjecture is now stated in more general terms, using tensors and the notion of tensor rank and it is still open since the 70s.
In this talk, we will discuss some recent progress on the study of Strassen's conjecture. In particular, we will focus on the case of symmetric tensors which correspond to homogeneous polynomials.