We show that critical parking trees conditioned to be fully parked converge in the scaling limits towards the Brownian growth-fragmentation tree, a self-similar Markov tree different from Aldous’ Brownian tree. As a by-product of our study, we prove that positive non-linear functional equations involving a catalytic variable display a universal polynomial exponent 5/2 at their singularity,...
Once put into suitable generating series, various enumerative invariants on Calabi-Yau threefolds are expected to possess modular properties, allowing to determine them uniquely from a few data points and giving powerful control on their asymptotic growth. This includes Gromov-Witten invariants in presence of a genus one fibration, Noether-Lefschetz invariants in presence of a K3 fibration, as...
We consider the implications of modular invariance for the spectrum of two-dimensional CFTs. For states with high energy this question was analyzed at a qualitative level by Cardy in 1986, but rigorous statements were almost entirely absent until the analysis (based on Tauberian theorems) by Mukhametzhanov and Zhiboedeov in 2019. In this talk we consider states with a very large spin, for...
Ideal triangulations of 3-manifolds with nonempty boundary were introduced by Thurston as an effective means of computing the complete hyperbolic structure on a cusped hyperbolic 3-manifold and its Dehn fillings. The combinatorics of the triangulations leads to gluing equations via Neumann-Zagier matrices, and these in turn lead to a plethora of quantum 3-manifold invariants. We will give a...
