**Data:**segunda-feira, 25 de março de 2019, às 10h00.

**Sala:**249-A

**Palestrante:**Jesús Castillo (Universidad de Extremadura)

**Título:**Complex interpolation and Banach space homology.

**Resumo:**We all know what a short exact sequence of Banach spaces is, that nontrivial exact sequences $0 \rightarrow \ell_2 \rightarrow X \rightarrow \ell_2 \rightarrow 0$ exist and that, among these, there is a peculiar one: the Kalton-Peck $Z_2$ sequence. Something that Homology says as $Ext(\ell_2, \ell_2)\neq 0$.

But there are exact sequence that are not short. And the question of whether nontrivial exact sequences $0 \rightarrow \ell_2 \rightarrow A \rightarrow B \rightarrow \ell_2 \rightarrow 0$ exist is what Homology formulates as $Ext^2(\ell_2, \ell_2)=0$ ? We will treat (a bit of) this question, we will show how the space $Z_2$ opens the door to let complex interpolation in and then we will see how this no-man's intermediate land between homology and complex interpolation brings new questions. We will try to glimpse their meaning and possible answers.

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