Matt Szczesny

Feynman Graphs, Rooted Trees, and Ringel-Hall Algebras

We construct symmetric monoidal categories

Supersymmetry of the chiral de Rham complex

{\mathcal{LRF}, \mathcal{LFG}}

CHIRAL DE RHAM COMPLEX AND ORBIFOLDS

of rooted forests and Feynman graphs. These categories closely resemble finitary abelian categories, and in particular, the notion of Ringel-Hall algebra applies. The Ringel-Hall Hopf algebras of

On the Hall algebra of coherent sheaves on P1 over F1

{\mathcal{LRF}, \mathcal{LFG}}

On the Hall algebra of semigroup representations over F_1

,