Thom series of contact singularities
  Thom polynomials measure how global topology forces singularities. The power of Thom polynomials predestine them to be a useful tool not only in differential topology, but also in algebraic geometry (enumerative geometry, moduli spaces) and algebraic combinatorics. The main obstacle of their widespread application is that only a few, sporadic Thom polynomials have been known explicitly. In this paper we develop a general method for calculating Thom polynomials of contact singularities. Along the way, relations with the equivariant geometry of (punctual, local) Hilbert schemes, and with iterated residue identities are revealed. 
L. M. Feh\'er, R. Rim\'anyi