Introduction to topological recursion – 1

Topological recursion is a remarkable universal recursive procedure that has been found in many enumerative geometry problems, from combinatorics of maps, to random matrices, Gromov-Witten invariants, Hurwitz numbers, Mirzakhani's hyperbolic volumes of moduli spaces, knot polynomials, conformal blocks, integrable systems. It is a recursion on the Euler characteristic, whence the name “topological” recursion. A`recursion needs an initial data: a spectral curve, and the recursion defines the sequence of invariants of that spectral curve. In this series of lectures, we will – define the topological recursion, spectral curves and their invariants, and illustrate it with examples.  
– introduce the Fock space formalism which proved to be very efficient for computing TR-invariants for the various classes of spectral curves.
– if time permits we will state recent results on the duality of “mixed” TR-invariants and the new recursion on the mixed invariants.