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Monday, March 28, 2016

**Abstract:** In the paper “Formal noncommutative symplectic geometry”, Maxim Kontsevich introduced three versions of cochain complexes GC_Com, GC_Lie and GC_As “assembled from” graphs with some additional structures. The graph complex GC_Com (resp. GC_Lie, GC_As) is related to the operad Com (resp. Lie, As) governing commutative (resp. Lie, associative) algebras. Although the graphs complexes GC_Com, GC_Lie and GC_As (and their generalizations) are easy to define, it is hard to get very much information about their cohomology spaces. In my talk, I will describe the links between these graph complexes (and their modifications) to the cohomology of the moduli spaces of curves, the group of outer automorphisms Out(F_r) of the free group F_r on r generators, the absolute Galois group Gal(bar{Q}/Q) of rationals, finite type invariants of tangles, and the homotopy groups of embedding spaces.