Alessandro Giacchetto
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View article: Matrix Correlators as Discrete Volumes of Moduli Space I: Recursion Relations, the BMN-limit and DSSYK
Matrix Correlators as Discrete Volumes of Moduli Space I: Recursion Relations, the BMN-limit and DSSYK Open
We show certain correlators in generic one-matrix models define a notion of ``discrete'' volumes of the moduli space of Riemann surfaces, generalizing the connection between random matrices and JT gravity. We prove they obey a discrete, Mi…
View article: A new spin on Hurwitz theory and ELSV via theta characteristics
A new spin on Hurwitz theory and ELSV via theta characteristics Open
We study spin Hurwitz numbers, which count ramified covers of the Riemann sphere with a sign coming from a theta characteristic. These numbers are known to be related to Gromov–Witten theory of Kähler surfaces and to representation theory …
View article: Symmetries of F-Cohomological Field Theories and F-Topological Recursion
Symmetries of F-Cohomological Field Theories and F-Topological Recursion Open
We define F-topological recursion (F-TR) as a non-symmetric version of topological recursion, which associates a vector potential to some initial data. We describe the symmetries of the initial data for F-TR and show that, at the level of …
View article: Relations on $\overline{\mathcal{M}}_{g,n}$ and the negative $r$-spin Witten conjecture
Relations on $\overline{\mathcal{M}}_{g,n}$ and the negative $r$-spin Witten conjecture Open
We construct and study various properties of a negative spin version of the Witten $r $ -spin class. By taking the top Chern class of a certain vector bundle on the moduli space of spin curves that parametrises $r $ -th roots of the an…
View article: The factorial growth of topological recursion
The factorial growth of topological recursion Open
We show that the n -point, genus- g correlation functions of topological recursion on any regular spectral curve with simple ramifications grow at most like $$(2g - 2 + n)!$$ as $$g \rightarrow \infty $$ , which is the expe…
View article: The spin Gromov–Witten/Hurwitz correspondence for $\mathbb{P}^{1}$
The spin Gromov–Witten/Hurwitz correspondence for $\mathbb{P}^{1}$ Open
We study the spin Gromov–Witten theory of \mathbb{P}^{1} . Using the standard torus action on \mathbb{P}^{1} , we prove that the associated equivariant potential can be expressed by means of operator formalism and satisfies the 2-BKP hiera…
View article: Length spectrum of large genus random metric maps
Length spectrum of large genus random metric maps Open
We study the length of short cycles on uniformly random metric maps (also known as ribbon graphs) of large genus using a Teichmüller theory approach. We establish that, as the genus tends to infinity, the length spectrum converges to a Poi…
View article: Les Houches lecture notes on moduli spaces of Riemann surfaces
Les Houches lecture notes on moduli spaces of Riemann surfaces Open
In these lecture notes, we provide an introduction to the moduli space of Riemann surfaces, a fundamental concept in the theories of 2D quantum gravity, topological string theory, and matrix models. We begin by reviewing some basic results…
View article: The factorial growth of topological recursion
The factorial growth of topological recursion Open
We show that the $n$-point, genus-$g$ correlation functions of topological recursion on any regular spectral curve with simple ramifications grow at most like $(2g - 2 + n)!$ as $g \rightarrow \infty$, which is the expected growth rate. Th…
View article: Can Transformers Do Enumerative Geometry?
Can Transformers Do Enumerative Geometry? Open
How can Transformers model and learn enumerative geometry? What is a robust procedure for using Transformers in abductive knowledge discovery within a mathematician-machine collaboration? In this work, we introduce a Transformer-based appr…
View article: Symmetries of F-cohomological field theories and F-topological recursion
Symmetries of F-cohomological field theories and F-topological recursion Open
We define F-topological recursion (F-TR) as a non-symmetric version of topological recursion, which associates a vector potential to some initial data. We describe the symmetries of the initial data for F-TR and show that, at the level of …
View article: Length spectrum of large genus random metric maps
Length spectrum of large genus random metric maps Open
We study the length of short cycles on uniformly random metric maps (also known as ribbon graphs) of large genus using a Teichmüller theory approach. We establish that, as the genus tends to infinity, the length spectrum converges to a Poi…
View article: Resurgent large genus asymptotics of intersection numbers
Resurgent large genus asymptotics of intersection numbers Open
In this paper, we present a novel approach for computing the large genus asymptotics of intersection numbers. Our strategy is based on a resurgent analysis of the $n$-point functions of such intersection numbers, which are computed via det…
View article: THE SPIN GROMOV–WITTEN/HURWITZ CORRESPONDENCE FOR P^1
THE SPIN GROMOV–WITTEN/HURWITZ CORRESPONDENCE FOR P^1 Open
We study the spin Gromov–Witten (GW) theory of P1. Using the standard torus action on P1, we prove that the associated equivariant potential can be expressed by means of operator formalism and satisfies the 2-BKP hierarchy. As a consequenc…
View article: Issue Information
Issue Information Open
Ferna ´ndez de BoBadilla (Singularity theory and algebraic geometry) J. Fine (Differential geometry, geometric analysis, and global analysis) a. Fink (Algebraic combinatorics) J. Fintzen (Representation theory and the Langlands corresponde…
View article: Topological recursion for Masur–Veech volumes
Topological recursion for Masur–Veech volumes Open
We 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. We show that the volumes MVg,n are the constant terms of a family of polynom…
View article: Around the Combinatorial Unit Ball of Measured Foliations on Bordered Surfaces
Around the Combinatorial Unit Ball of Measured Foliations on Bordered Surfaces Open
The volume $\mathcal {B}_{\sum }^{\textrm {comb}}({\mathbb {G}})$ of the unit ball—with respect to the combinatorial length function $\ell _{{\mathbb {G}}}$—of the space of measured foliations on a stable bordered surface $\sum $ appears a…
View article: The Spin Gromov-Witten/Hurwitz correspondence for $\mathbb{P}^1$
The Spin Gromov-Witten/Hurwitz correspondence for $\mathbb{P}^1$ Open
We study the spin Gromov-Witten (GW) theory of $\mathbb{P}^1$. Using the standard torus action on $\mathbb{P}^1$, we prove that the associated equivariant potential can be expressed by means of operator formalism and satisfies the 2-BKP hi…
View article: Relations on $\overline{\mathcal{M}}_{g,n}$ and the negative $r$-spin Witten conjecture
Relations on $\overline{\mathcal{M}}_{g,n}$ and the negative $r$-spin Witten conjecture Open
We construct and study various properties of a negative spin version of the Witten $ r $-spin class. By taking the top Chern class of a certain vector bundle on the moduli space of twisted spin curves that parametrises $ r $-th roots of th…
View article: Shifted Witten classes and topological recursion
Shifted Witten classes and topological recursion Open
The Witten $r$-spin class defines a non-semisimple cohomological field theory. Pandharipande, Pixton and Zvonkine studied two special shifts of the Witten class along two semisimple directions of the associated Dubrovin--Frobenius manifold…
View article: An intersection-theoretic proof of the Harer-Zagier formula
An intersection-theoretic proof of the Harer-Zagier formula Open
We provide an intersection-theoretic formula for the Euler characteristic of the moduli space of smooth curves. This formula reads purely in terms of Hodge integrals and, as a corollary, the standard calculus of tautological classes gives …
View article: An intersection-theoretic proof of the Harer-Zagier formula
An intersection-theoretic proof of the Harer-Zagier formula Open
We provide an intersection-theoretic formula for the Euler characteristic of\nthe moduli space of smooth curves. This formula reads purely in terms of Hodge\nintegrals and, as a corollary, the standard calculus of tautological classes\ngiv…
View article: Around the combinatorial unit ball of measured foliations on bordered surfaces
Around the combinatorial unit ball of measured foliations on bordered surfaces Open
The volume $\mathscr{B}_Σ^{\rm comb}(\mathbb{G})$ of the unit ball -- with respect to the combinatorial length function $\ell_{\mathbb{G}}$ -- of the space of measured foliations on a stable bordered surface $Σ$ appears as the prefactor of…
View article: Around the combinatorial unit ball of measured foliations on bordered surfaces
Around the combinatorial unit ball of measured foliations on bordered surfaces Open
The volume $\mathscr{B}_{\Sigma}^{{\rm comb}}(\mathbb{G})$ of the unit ball -- with respect to the combinatorial length function $\ell_{\mathbb{G}}$ -- of the space of measured foliations on a stable bordered surface $\Sigma$ appears as th…
View article: A new spin on Hurwitz theory and ELSV via theta characteristics
A new spin on Hurwitz theory and ELSV via theta characteristics Open
We study spin Hurwitz numbers, which count ramified covers of the Riemann sphere with a sign coming from a theta characteristic. These numbers are known to be related to Gromov-Witten theory of Kähler surfaces and to representation theory …
View article: On the Kontsevich geometry of the combinatorial Teichmüller space
On the Kontsevich geometry of the combinatorial Teichmüller space Open
For bordered surfaces S, we develop a complete parallel between the geometry of the combinatorial Teichmüller space $T_S^{comb}$ equipped with Kontsevich symplectic form $ω_K$, and then the usual Weil-Petersson geometry of Teichmüller spac…
View article: Masur-Veech volumes and intersection theory: the principal strata of\n quadratic differentials
Masur-Veech volumes and intersection theory: the principal strata of\n quadratic differentials Open
We describe a conjectural formula via intersection numbers for the\nMasur-Veech volumes of strata of quadratic differentials with prescribed zero\norders, and we prove the formula for the case when the zero orders are odd. For\nthe princip…
View article: Topological recursion for Masur-Veech volumes
Topological recursion for Masur-Veech volumes Open
We study the Masur-Veech volumes $MV_{g,n}$ of the principal stratum of the moduli space of quadratic differentials of unit area on curves of genus $g$ with $n$ punctures. We show that the volumes $MV_{g,n}$ are the constant terms of a fam…