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A simplicial and categorical background for Hopf algebras in number theory and physics

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Ralph Martin Kaufmann
Purdue University, West Lafayette/MPIM
Thu, 2019-07-25 15:00 - 16:00
MPIM Lecture Hall
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We will discuss how simplicial  and categorical structures lead to Hopf algebras.

In particular, we will focus on Joyal duality to give a simple explanation of the co-product given by Goncharov
for multi-zeta values and its graphical depiction. In this setting, co-actions also appear naturally. We further show that
his type of Hopf algebracomes from a categorical setup, where the product is a monoidal product and the co-product is
dual to the partial productthat is  given by composition of morphisms, providing a simple "raison d'être" for these
"prima vista" complicated co-products. In this setting, we see the analogous structure of the Hopf algebra of Goncharov
and those of Connes and Kreimer.
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