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Thom polynomials measure how global topology forces singularities. The powerof Thom polynomials predestine them to be a useful tool not only indifferential topology, but also in algebraic geometry (enumerative geometry,moduli spaces) and algebraic combinatorics. The main obstacle of theirwidespread application is that only a few, sporadic Thom polynomials have beenknown explicitly. In this paper we develop a general method for calculatingThom polynomials of contact singularities. Along the way, relations with theequivariant geometry of (punctual, local) Hilbert schemes, and with iteratedresidue identities are revealed.

Thom series of contact singularities