The combinatorial description of the moduli space of curves in terms of ribbon graphs was one of the crucial ingredients in Kontsevich’s proof of Witten’s conjecture. The same model was used by

https://indico.math.cnrs.fr/event/15338/

https://indico.math.cnrs.fr/event/15723/

https://indico.math.cnrs.fr/event/15786/

https://indico.math.cnrs.fr/event/15345/

Quantum field theories (QFTs) provide a very effective framework for describing relativistic quantum systems with an infinite number of degrees of freedom. In particular, their setting allows one to provide expressions for

https://indico.math.cnrs.fr/event/15718/

https://indico.math.cnrs.fr/event/15771/

https://indico.math.cnrs.fr/event/15777/

https://indico.math.cnrs.fr/event/15830/