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Abstract |
Topological recursion, takes as inpout data a "spectral curve" S (ex: an algebraic equation
P(x,y)=0 with P a polynomial, but can be more general), and associates to it an infinite
sequence of differential n-forms W_{g,n}(S), called the invariants of the spectral curve. The
scalar invariants n=0 are often denoted F_g(S)=W_{g,0}(S). Many invariants of enumerative
geometry are special cases of these, like Gromov-Witten invariants, Hurwitz numbers,...
The formal series of scalar invariants is formally like a Tau-function $\Tau(S)=exp{\sum_g
F_g(S)}$, and has OPE and Ward indentities that enables to interpret them as heavy limit
asymptotic expansion of conformal blocks in a 2dCFT on a surface.
We shall make a short presentation of the topological recursion, and its application to
Mirzakhani's recursion, and to Liouville 2dCFT.
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