I want to explain a connection between two topics in algebraic geometry: (a) Moduli problems: parametrizing quotients of a vector bundle (Quot scheme). (b) Structures in enumerative geometry: topological quantum field theory (TQFT); algebraic cobordism (of complex manifolds equipped with a vector bundle). The connection is that the Quot schemes that are finite fit into interesting enumerative structures. In particular: (1) On algebraic curves, the points of these Quot schemes are counted by formulas coming from a TQFT. (2) On algebraic surfaces, these points are conjecturally counted by formulas coming from algebraic cobordism. These finite Quo