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Quadratic Relations in Feynman Categories

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Speaker: 
Ralph Kaufmann
Affiliation: 
Purdue University, West Lafayette
Date: 
Tue, 2018-02-27 14:00 - 15:00
Location: 
MPIM Lecture Hall

I will start with a brief introduction to Feynman categories, and then explore the consequences of
quadratic relations for the morphisms in Feynman categories.

In the first part of the talk, I show how this leads to cubical complexes and prove that in this
way both the complex for moduli spaces of curves and the cubical complexes for Cutkosky rules
and calculations for Outer space arise naturally from push-forwards.
In the second part, I study generalizations of the quadradtic relations, which naturally lead
us to quantum groups in the setting of quadratic algebras provided by Manin.
I end with speculations on the generalization of quantum master equations to this setting.

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