  We develop a representation theoretic technique for detecting closed orbits
that is applicable in all characteristics. Our technique is based on Kempf's
theory of optimal subgroups and we make some improvements and simplify the
theory from a computational perspective. We exhibit our technique in many
examples and in particular, give an algorithm to decide if a symmetric
polynomial in $n$-variables has a closed ${\rm SL}_n$ orbit.
  As an important application, we prove exponential lower bounds on the maximal
degree of a system of generators of invariant rings for two actions that are
important from the perspective of Geometric Complexity Theory (GCT). The first
is the action of ${\rm SL}(V)$ on ${\rm Sym}^3(V)^{\oplus 3}$, the space of
3-tuples of cubic forms, and the second is the action of ${\rm SL}(V) \times
{\rm SL}(W) \times {\rm SL}(Z)$ on the tensor space $(V \otimes W \otimes
Z)^{\oplus 5}$. In both these cases, we prove an exponential lower degree bound
for a system of invariants that generate the invariant ring or that define the
null cone.
