Aarhus University Seal / Aarhus Universitets segl

Arxived article on topological recursion

Jørgen Ellegaard Andersen presents a new result with collaborators on arXiv

2019.05.27 | Jane Jamshidi

Professor Jørgen Ellegaard Andersen has jointly with his international collaborators Gaëtan Borot, Séverin Charbonnier, Vincent Delecroix, Alessandro Giacchetto, Danilo Lewanski & Campbell Wheeler submitted a new result on arXiv entitled " Topological recursion for Masur-Veech volumes".

Here they study the Masur–Veech volumes MVg,n of the principal stratum of the moduli space of quadratic differentials of unit area on curves of genus g with n punctures. They show that the volumes MVg,n are the constant terms of a family of polynomials in n variables governed by the topological recursion/Virasoro constraints. This is equivalent to a formula giving these polynomials as a sum over stable graphs, and retrieves a result proved by combinatorial arguments of a paper in preparation by  V. Delecroix, E. Goujard, P. Zograf, and A. Zorich. The method in this arXived paper is different: it relies on the geometric recursion and its application to statistics of hyperbolic lengths of multicurves developed in a previous paper by J.E. Andersen, G. Borot, and N. Orantin from 2017.

In the present arXived paper J.E. Andersen and collaborators also obtain an expression of the area Siegel–Veech constants in terms of hyperbolic geometry. The topological recursion allows numerical computations of Masur–Veech volumes, and thus of area Siegel–Veech constants, for low g and n, which leads us to propose conjectural formulas for low g but all n.   

Link to the paper on arXiv: https://arxiv.org/pdf/1905.10352.pdf