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$Dg$-categories have been very important in Algebraic Geometry for a really long time; but they are not without their issues. In order to solve these, current researchers have been turning to different models of $\infty$-categories for inspiration. Enriched $\infty$-categories, $dg$-Segal categories, enriched quasi-categories... Following this flourishing field, in this talk we will define a new model for $dg$-categories inspired in Rezk's complete Segal spaces model for $\infty$-categories. During this talk we will define $dg$-Segal spaces, give its relationship to classical Segal spaces, use this to define complete $dg$-Segal spaces and its model structure and give a sketch of the proof of its equivalence to Tabuada's model structure of $dg$-categories. If time allows, we will say a word about some possible refinements of the model, and mention some work in progress surrounding its relationship to Mertens and Borges Marques' model of $dg$-Segal spaces.

Zoom uygulaması Bilim Akademisi tarafından sağlanmaktadır./Zoom link is provided by The Science Academy.