Gaëtan Borot
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View article: Whittaker vectors at finite energy scale, topological recursion and Hurwitz numbers
Whittaker vectors at finite energy scale, topological recursion and Hurwitz numbers Open
We upgrade the results of Borot–Bouchard–Chidambaram–Creutzig [BBCC24] to show that the Gaiotto vector in pure supersymmetric gauge theory admits an analytic continuation with respect to the energy scale (which can therefore be taken to …
View article: Taking limits in topological recursion
Taking limits in topological recursion Open
When does topological recursion applied to a family of spectral curves commute with taking limits? This problem is subtle, especially when the ramification structure of the spectral curve changes at the limit point. We provide sufficient (…
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: 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: On ELSV-type formulae and relations between Ω-integrals via deformations of spectral curves
On ELSV-type formulae and relations between Ω-integrals via deformations of spectral curves Open
View article: Topological recursion for fully simple maps from ciliated maps
Topological recursion for fully simple maps from ciliated maps Open
We solve a conjecture from the first and third authors that claims that fully simple maps, which are maps with non self-intersecting disjoint boundaries, satisfy topological recursion for the exchanged spectral curve \\((y, x)\\), making u…
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: Fay Identities of Pfaffian Type for Hyperelliptic Curves
Fay Identities of Pfaffian Type for Hyperelliptic Curves Open
We establish identities of Pfaffian type for the theta function associated with twice or half the period matrix of a hyperelliptic curve. They are implied by the large size asymptotic analysis of exact Pfaffian identities for expectation v…
View article: A Note on BKP for the Kontsevich Matrix Model with Arbitrary Potential
A Note on BKP for the Kontsevich Matrix Model with Arbitrary Potential Open
We exhibit the Kontsevich matrix model with arbitrary potential as a BKP tau-function with respect to polynomial deformations of the potential. The result can be equivalently formulated in terms of Cartan-Plücker relations of certain avera…
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: Higher Airy Structures, 𝒲 Algebras and Topological Recursion
Higher Airy Structures, 𝒲 Algebras and Topological Recursion Open
We define higher quantum Airy structures as generalizations of the Kontsevich–Soibelman quantum Airy structures by allowing differential operators of arbitrary order (instead of only quadratic). We construct many classes of examples of hig…
View article: Whittaker vectors at finite energy scale, topological recursion and Hurwitz numbers
Whittaker vectors at finite energy scale, topological recursion and Hurwitz numbers Open
We upgrade the results of Borot--Bouchard--Chidambaram--Creutzig to show that the Gaiotto vector in $4d$ $\mathcal{N} = 2$ pure supersymmetric gauge theory admits an analytic continuation with respect to the energy scale (which can therefo…
View article: Whittaker vectors for $$\mathcal {W}$$-algebras from topological recursion
Whittaker vectors for $$\mathcal {W}$$-algebras from topological recursion Open
We identify Whittaker vectors for $$\mathcal {W}^{\textsf{k}}(\mathfrak {g})$$ -modules with partition functions of higher Airy structures. This implies that Gaiotto vectors, describing the fundamental class in the equivariant co…
View article: The ABCD of topological recursion
The ABCD of topological recursion Open
View article: Nesting statistics in the $O(n)$ loop model on random maps of arbitrary topologies
Nesting statistics in the $O(n)$ loop model on random maps of arbitrary topologies Open
We pursue the analysis of nesting statistics in the O(n) loop model on random maps, initiated for maps with the topology of disks and cylinders by Borot, Bouttier and Duplantier (2016), here for arbitrary topologies. For this purpose, we r…
Asymptotic expansion of matrix models in the multi-cut regime Open
View article: On ELSV-type formulae and relations between $Ω$-integrals via deformations of spectral curves
On ELSV-type formulae and relations between $Ω$-integrals via deformations of spectral curves Open
The general relation between Chekhov-Eynard-Orantin topological recursion and the intersection theory on the moduli space of curves, the deformation techniques in topological recursion, and the polynomiality properties with respect to defo…
View article: Fay Identities of Pfaffian Type for Hyperelliptic Curves
Fay Identities of Pfaffian Type for Hyperelliptic Curves Open
We establish identities of Pfaffian type for the theta function associated with twice or half the period matrix of a hyperelliptic curve. They are implied by the large size asymptotic analysis of exact Pfaffian identities for expectation v…
View article: Nesting Statistics in the O(n) Loop Model on Random Planar Maps
Nesting Statistics in the O(n) Loop Model on Random Planar Maps Open
View article: Taking limits in topological recursion
Taking limits in topological recursion Open
When does topological recursion applied to a family of spectral curves commute with taking limits? This problem is subtle, especially when the ramification structure of the spectral curve changes at the limit point. We provide sufficient (…
View article: A Note on BKP for the Kontsevich Matrix Model with Arbitrary Potential
A Note on BKP for the Kontsevich Matrix Model with Arbitrary Potential Open
We exhibit the Kontsevich matrix model with arbitrary potential as a BKP tau-function with respect to polynomial deformations of the potential. The result can be equivalently formulated in terms of Cartan-Plücker relations of certain avera…
View article: Higher Airy structures and topological recursion for singular spectral curves
Higher Airy structures and topological recursion for singular spectral curves Open
We give elements towards the classification of quantum Airy structures based on the W(\mathfrak{gl}_r) -algebras at self-dual level based on twisted modules of the Heisenberg VOA of \mathfrak{gl}_r for twists by arbitrary elements of the W…
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: Double Hurwitz numbers: polynomiality, topological recursion and intersection theory
Double Hurwitz numbers: polynomiality, topological recursion and intersection theory Open
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: Functional relations for higher-order free cumulants
Functional relations for higher-order free cumulants Open
We establish the functional relations between generating series of higher-order free cumulants and moments in higher-order free probability, solving an open problem posed fifteen years ago by Collins, Mingo, Śniady and Speicher. We propose…
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: Topological recursion for fully simple maps from ciliated maps
Topological recursion for fully simple maps from ciliated maps Open
Ordinary maps satisfy topological recursion for a certain spectral curve $(x, y)$. We solve a conjecture from arXiv:1710.07851 that claims that fully simple maps, which are maps with non self-intersecting disjoint boundaries, satisfy topol…