In this talk, we draw a connection between vanishing
Hessian and wildness: a form is wild when its smoothable
rank is strictly larger than its border rank. This
discrepancy is caused by the difference between the
limit of spans of zero-dimensional schemes and the span
of their flat limit. Inspired by recent work on border
apolarity of Buczyńska and Buczyński, we study the
border varieties of sums of powers of two infinite series
of wild forms (with a combinatorial flavor) in the
corresponding multigraded Hilbert scheme. 
This is joint work with H. Huang and M. Michałek.