Alessandro Giacchetto

TL;DR: In this paper, the Masur-Veech volumes of the moduli space of quadratic differentials of unit area on curves of genus $g$ with $n$ punctures were studied and proved to be constant terms of a family of polynomials in variables governed by the topological recursion/Virasoro constraints.

TL;DR: In this paper, a conjectural formula via intersection numbers for the Masur-Veech volumes of strata of quadratic differentials with prescribed zero orders is presented.

TL;DR: In this paper, the authors study the combinatorial Teichm\"uller space and construct on it global coordinates, analogous to the Fenchel-Nielsen coordinates on the ordinary Teichmculler spaces, and prove that these coordinates form an atlas with piecewise linear transition functions.

TL;DR: In this article, the authors studied spin Hurwitz numbers, which count ramified covers of the Riemann sphere with a sign coming from a theta characteristic, and derived a spectral curve which they conjecture computes spin-Hurwitz numbers via a new type of topological recursion.

TL;DR: In this article , Pandharipande, Pixton and Zvonkine studied two special shifts of the Witten class along two semisimple directions of the associated Dubrovin-Frobenius manifold using the Givental-Teleman reconstruction theorem and showed that the R -matrix and the translation of these two speci c shifts can be constructed from the solutions of two differential equations that generalise the classical Airy differential equation.