  Certain foams and relations on them are introduced to interpret functors and
natural transformations in categories of representations of iterated wreath
products of cyclic groups of order two. We also explain how patched surfaces
with defect circles and foams relate to separable field extensions and Galois
theory and explore a relation between overlapping foams and Sylvester double
sums. In the appendix, joint with Lev Rozansky, we compare traces in
two-dimensional TQFTs coming from matrix factorizations with those in field
extensions.
