Abstract:
The Grothendieck–Teichmueller group (GT) appears in many different parts
of mathematics: in the theory of moduli spaces of algebraic curves,
in number theory, in the theory of motives, in the theory of deformation
quantization etc. Using recent breakthrough theorems by Thomas Willwacher,
we argue that GT controls the deformation theory of a line in
the complex plane when one understands these geometric structures
via their associated operads of (compactified) configuration
spaces. Applications to Poisson geometry, deformation quantization,
and Batalin–Vilkovisky formalism are discussed.
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