Large genus asymptotics for intersection numbers and principal strata volumes of quadratic differentials

Aggarwal, Amol

doi:10.1007/s00222-021-01059-9

Cited by 8 publications

(7 citation statements)

References 32 publications

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“…We also note that the DGZZ conjecture is proved by Aggarwal [1]. Actually, Aggarwal [1] proves a stronger result that Conjecture A still holds when "n < C log(g)" of ( 15) is replaced by "n = o g 1/2 "; so due to Aggarwal's theorem, the number C in Conjecture A can be an arbitrarily given positive number. The first result of this paper is a novel proof of the following theorem, which we call the DGZZ-A theorem.…”

Section: Introduction and Statements Of The Resultsmentioning

confidence: 82%

“…Let g, n be non-negative integers satisfying the stability condition (1) 2g − 2 + n > 0, and M g,n the Deligne-Mumford moduli space [11] of stable algebraic curves of genus g with n distinct marked points. Denote by L j the jth cotangent line bundle on M g,n , j = 1, .…”

Section: Introduction and Statements Of The Resultsmentioning

confidence: 99%

“…Remark 1. Both Aggarwal's proof [1] and our proof use the Witten-Kontsevich theorem. However, unlike Aggarwal's proof where the Virasoro constraints (10) are used, our proof uses ( 17)- (18).…”

Section: Introduction and Statements Of The Resultsmentioning

confidence: 99%

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On the large genus asymptotics of psi-class intersection numbers

Guo¹,

Yang²

2021

Preprint

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Section: Introduction and Statements Of The Resultsmentioning

confidence: 82%

Section: Introduction and Statements Of The Resultsmentioning

confidence: 99%

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On the large genus asymptotics of psi-class intersection numbers

Guo¹,

Yang²

2021

Preprint

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“…ILW-type) integrability properties of such linear Hodge integrals. Moreover, Aggarwal [1] provided their large g limit behaviour, originally conjectured by Aggarwal-Delecroix-Goujard-Zograf-Zorich.…”

Section: Theorem 16 ([5]mentioning

confidence: 88%

“…This concludes the proof of Theorem 1.2. 1 The relation χ g,n+1 = −(2g − 2 + n)χ g,n easily follows from a short exact sequence involving mapping class groups (see [12,Section 6]). Here we provide another proof that only uses the intersection-theoretic expression for χ g,n .…”

Section: Proofsmentioning

confidence: 99%

An intersection-theoretic proof of the Harer-Zagier formula

Giacchetto¹,

Lewański²,

Norbury³

2021

Preprint

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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 a new short proof of the Harer-Zagier formula. Our result is based on the Gauss-Bonnet formula, and on the observation that a certain parametrisation of the Ω-class -the Chern class of the universal r-th root of the twisted log canonical bundle -provides the Chern class of the log tangent bundle to the moduli space of smooth curves. Being Ω-classes by now employed in many enumerative problems, mostly recently found and at times surprisingly different from each other, we dedicate some work to produce an extensive list of their general properties: extending existing ones, finding new ones, and writing down some only known to the experts.

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Resurgent Asymptotics of Jackiw–Teitelboim Gravity and the Nonperturbative Topological Recursion

Eynard,

Garcia-Failde,

Gregori

et al. 2024

Ann. Henri Poincaré

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Jackiw–Teitelboim dilaton quantum gravity localizes on a double-scaled random-matrix model, whose perturbative free energy is an asymptotic series. Understanding the resurgent properties of this asymptotic series, including its completion into a full transseries, requires understanding the nonperturbative instanton sectors of the matrix model for Jackiw–Teitelboim gravity. The present work addresses this question by setting-up instanton calculus associated with eigenvalue tunneling (or ZZ-brane contributions), directly in the matrix model. In order to systematize such calculations, a nonperturbative extension of the topological recursion formalism is required—which is herein both constructed and applied to the present problem. Large-order tests of the perturbative genus expansion validate the resurgent nature of Jackiw–Teitelboim gravity, both for its free energy and for its (multi-resolvent) correlation functions. Both ZZ and FZZT nonperturbative effects are required by resurgence, and they further display resonance upon the Borel plane. Finally, the resurgence properties of the multi-resolvent correlation functions yield new and improved resurgence formulae for the large-genus growth of Weil–Petersson volumes.

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Large genus asymptotics for intersection numbers and principal strata volumes of quadratic differentials

Cited by 8 publications

References 32 publications

On the large genus asymptotics of psi-class intersection numbers

On the large genus asymptotics of psi-class intersection numbers

An intersection-theoretic proof of the Harer-Zagier formula

Resurgent Asymptotics of Jackiw–Teitelboim Gravity and the Nonperturbative Topological Recursion

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