## Lipschitz geometry of operator spaces and Lipschitz-free operator spaces

Abstract: While the nonlinear geometry of Banach spaces has been extensively studied (especially in the past few decades), the nonlinear geometry of its noncommutative counterpart, i.e., of operator spaces, has been neglected until very recently. In this talk, I will discuss some recent developments in this field. In particular, I will introduce the notion of almost complete Lipschitz embeddability between operator spaces and explain why this leads to a nontrivial nonlinear theory. For that, Lipschitz free spaces of operator spaces will play an important role. (This is a joint with with Javier Alejandro Chávez-Domínguez and Thomas Sinclair).

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