Multiplicity of the fat point in differential algebra

While the concept of multiplicity is essential in the intersection theory, there is no such analogue for solutions of differential algebraic equations. In this talk I will motivate the definition of the multiplicity of a solution as the growth rate of the multiplicities of its truncations by considering the differential ideal of the fat point $x^m$. At the end I will briefly discuss some combinatoric connections between the multiplicity structure of the arc space of a fat point and Rogers-Ramanujan partition identities.

This is an ongoing project with Gleb Pogudin.