  We exhibit infinitely many, explicit special Lagrangian isolated
singularities that admit no asymptotically conical special Lagrangian
smoothings. The existence/ nonexistence of such smoothings is an important
component of the current efforts to understand which singular special
Lagrangians arise as limits of smooth special Lagrangians.
  We also use soft methods from symplectic geometry (the relative version of
the h--principle) and tools from algebraic topology to prove (both positive and
negative) results about Lagrangian desingularizations of Lagrangian
submanifolds with isolated singularities; we view the Lagrangian
desingularization problem as the natural soft analogue of the special
Lagrangian smoothing problem.
