We introduce a new collection of CohFTs, the \({\Theta}^{r,s}\)-classes, and show that their descendant potential is an \(r\)-KdV tau function, is computed by topological recursion, and satisfies \({\mathcal{W}}\)-constraints.
We prove the large genus asymptotics for Witten–Kontsevich, Norbury’s, and \(r\)-spin intersection numbers.
We study the geometry of the combinatorial moduli spaces, providing a completely geometric proof of Witten’s conjecture.
We prove that topological recursion is Gevrey-2.
We use transformer to compute and understand recursive patterns in \(\psi\)-class intersection numbers, showing that the model learns key mathematical features from the data.
We introduce F-topological recursion and show that the descendant theory of F-CohFTs in the Givental orbit are compute by F-topological recursion.
We prove that the lenght spectrum of random metric maps converges to a Poisson point process in the large genus limit.
We prove the GW/H correspondence for the spin projective line, a first step toward the computation of GW invariants of surfaces of general type.
We construct a negative \(r\)-spin cohomological field theory, the \(r\)-spin \({\Theta}\)-class, prove topological recursion and \({\mathcal{W}}\)-constraints, and derive tautological relations via Teleman’s classification.
We deduce Witten’s \(r\)-spin conjecture from the connection between Givental’s formalism and topological recursion.
We compute the Euler charcteristic of the moduli space of curves via Chern–Gauss–Bonnet and Hodge integrals.
We study the \(L^p\)-integrability of the volume of the unit ball in the space of measured foliations.
We study spin Hurwitz numbers, which count ramified covers of the Riemann sphere with a sign coming from a theta characteristic. We conjecture a topological recursion governing these counts, and prove equivalence with an ELSV formula.
We prove that the descendant integrals of the Segre class of the quadratic Hodge bundle are computed by topological recursion.
We study the Masur–Veech volumes of quadratic differentials, showing they correspond to constant terms of polynomials determined by topological recursion/Virasoro constraints.
Lecture notes on the moduli space of curves, cohomological field theories, and topological recursion.