Groupe d’études et de recherche en analyse des décisions

# Topological recursion

## Bertrand Eynard – CPT, CEA Saclay, France

Topological recursion is an ubiquitous and universal recursive relationship that has appeared in various domains of mathematics and physics: volumes of moduli spaces, coefficients of asymptotic expansions in random matrix theory, Hurwitz numbers, Jones polynomials, Gromov-Witten invariants, and many other combinatorial objects, all mysteriously satisfy the same relation. Moreover, this recursion relation is effective: it allows an actual computation. This recursion has been axiomatized into a definition of some "new invariants" of curves. In this lecture we shall introduce the topological recursion, illustrate it on examples and mention its beautiful properties.