Benjamin C. Ward

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math.AT2024

Schwarz Modular Operads Revisited: $SM = S \circ M$

Ralph M. Kaufmann, Benjamin C. Ward

We prove that the Feynman category encoding Schwarz's variant of modular operads is Koszul. Our proof uses a generalization of the theory of distributive laws to the groupoid color…

math.AT2023

Stirling Decomposition of Graph Homology in Genus 1

Benjamin C. Ward

We prove that commutative graph homology in genus $g = 1$ with $n \geq 3$ markings has a direct sum decomposition whose summands have rank given by Stirling numbers of the first kind.…

Schwarz Modular Operads Revisited: SM=S∘M

Stirling Decomposition of Graph Homology in Genus 1

Schwarz Modular Operads Revisited: $SM = S \circ M$