Border subrank via a generalised Hilbert-Mumford criterion

The subrank of a bilinear map is the maximal number of independent scalar multiplications that can be linearly reduced to the bilinear map. Given a sufficiently general complex nxnxn tensor, we give an upper bound on the growth rate for the border subrank. Since this matches the growth rate for the generic (non-border) subrank recently established by Derksen-Makam-Zuiddam, we find that the generic border subrank has the same growth rate. In our proof, we use a generalisation of the Hilbert-Mumford criterion that we believe will be of independent interest. This talk is based on joint work with Chia-Yu Chang, Jan Draisma and Filip Rupniewski.