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Title:
The ubiquity of operadic calculus
Speaker:
Abstract:
There are basically two ways to do higher algebra: with model or higher categories or with operadic calculus. In the latter case, unlike in the former case, one gets explicit formulas which allow one to study questions like formality properties for instance. Operadic calculus provide us with seminal tools like the bar-cobar constructions, infinity-morphisms and the homotopy transfer theorem that lie at the core of special sequences, cyclic homology, rational homotopy theory and the Batalin--Vilkovisky formalism for instance. In this talk, I will try to review the present state of the art in this domain and to present some striking new results in universal algebra (Dotsenko—Tamaroff), rational homotopy theory (Campos—Petersen—Robert-Nicoud—Wierstra), gauge theory (Dotsenko—Shadrin—Vallette). For instance, I will explain how the operadic calculus can be extended from operads to properads (Hoffbeck—Leray—Vallette) in order to treat the homotopy properties of bialgebras, like involutive Lie bialgebras (Cieliebak—Fukaya—Latschev).
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