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Monday, January 29, 2018

**Abstract:** The computation of the pointed endomorphisms of $\mathbb P^1$ gives a first approximation to the zeroth stable homotopy group of the motivic sphere. In this introductory talk, following Cazanave, I’ll give some examples of a basic construction which associates a bilinear form to a rational function $\mathbb P^1 \rightarrow \mathbb P^1$. This will hint at a reason for the appearance of Grothendieck-Witt groups in stable motivic homotopy theory.