Formal rigidity of singular foliations around fixed points

In mathematics, rigidity questions arise in various settings. For instance, given a Lie algebra structure $\mu$ on a finite-dimensional vector space $V$, seen as a bilinear map, it is natural to ask when all nearby Lie algebra structures are related to $\mu$ by a linear automorphism of $V$. In geometry, similar questions arise when dealing with Lie algebra actions or Poisson structures, for which various results have been obtained. I will discuss the rigidity question for singular foliations, and show that analytic foliations are formally rigid around fixed points with semisimple isotropy Lie algebra, using Lie $n$-algebroids.