# Geometria em Lisboa Seminar

### The Stable Symplectic Category and a Conjecture of Kontsevich

Motivated by his work on deformation quantization and his computations of Feynman integrals, Kontsevich conjectured that a certain group (related to the Grothendieck Teichmuller group) acts on the moduli space of quantum field theories. Even though this moduli space is not well-defined in general, we will show that a stable version of this space makes sense and can be identified as a space that represents an interesting cohomology theory. In addition, we will show that a solvable quotient of the Grothendieck-Teichmuller group acts on the stable moduli space, and as such, it can be identified with an algebraic functor of the underlying cohomology theory.

Current organizer: Rosa Sena Dias