Shannon and joint entropy are recast as sums of infinitesimal dilogarithm brackets, and the five-term dilogarithm is deformed to the four-term infinitesimal dilogarithm via dual numbers.
Foams, iterated wreath products, field extensions and Sylvester sums
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abstract
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.
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Diagrammatics of information
Shannon and joint entropy are recast as sums of infinitesimal dilogarithm brackets, and the five-term dilogarithm is deformed to the four-term infinitesimal dilogarithm via dual numbers.