scholarly journals Buryak–Okounkov Formula for the n-Point Function and a New Proof of the Witten Conjecture

2020 ◽  
Author(s):  
Alexander Alexandrov ◽  
Francisco Hernández Iglesias ◽  
Sergey Shadrin
Keyword(s):  
Moduli Spaces ◽  
Integrable Systems ◽  
Intersection Theory ◽  
Intersection Numbers ◽  
Point Function ◽  
Moduli Spaces Of Curves ◽  
Witten Conjecture

Abstract We identify the formulas of Buryak and Okounkov for the $n$-point functions of the intersection numbers of psi-classes on the moduli spaces of curves. This allows us to combine the earlier known results and this one into a principally new proof of the famous Witten conjecture/Kontsevich theorem, where the link between the intersection theory of the moduli spaces and integrable systems is established via the geometry of double ramification cycles.

scholarly journals New results of intersection numbers on moduli spaces of curves

2007 ◽  
Vol 104 (35) ◽  
pp. 13896-13900
Author(s):  
K. Liu ◽  
H. Xu
Keyword(s):  
Moduli Spaces ◽  
Intersection Numbers ◽  
Moduli Spaces Of Curves

scholarly journals New properties of the intersection numbers on moduli spaces of curves

2007 ◽  
Vol 14 (6) ◽  
pp. 1041-1054 ◽  
Author(s):  
Kefeng Liu ◽  
Hao Xu
Keyword(s):  
Moduli Spaces ◽  
Intersection Numbers ◽  
Moduli Spaces Of Curves

scholarly journals Towards large genus asymptotics of intersection numbers on moduli spaces of curves

2015 ◽  
Vol 25 (4) ◽  
pp. 1258-1289 ◽  
Author(s):  
Maryam Mirzakhani ◽  
Peter Zograf
Keyword(s):  
Moduli Spaces ◽  
Intersection Numbers ◽  
Moduli Spaces Of Curves ◽  
Large Genus

scholarly journals Counting Non-Crossing Permutations on Surfaces of any Genus

10.37236/9890 ◽  
2021 ◽  
Vol 28 (4) ◽  
Author(s):  
Norman Do ◽  
Jian He ◽  
Daniel V. Mathews
Keyword(s):  
Moduli Spaces ◽  
Intersection Numbers ◽  
Moduli Spaces Of Curves

Given a surface with boundary and some points on the boundary, a polygon diagram is a way to connect those points as vertices of non-overlapping polygons on the surface. Such polygon diagrams represent non-crossing permutations on the surface. If only bigons are allowed, then one obtains the notion of arc diagrams, whose enumeration is known to have a rich structure. We show that the count of polygon diagrams on surfaces with any genus and number of boundary components exhibits similar structure. In particular it is almost polynomial in the number of points on the boundary components, and the leading coefficients of those polynomials are intersection numbers on compactified moduli spaces of curves.

scholarly journals The n-point functions for intersection numbers on moduli spaces of curves

2011 ◽  
Vol 15 (5) ◽  
pp. 1201-1236 ◽  
Author(s):  
Kefeng Liu ◽  
Hao Xu
Keyword(s):  
Moduli Spaces ◽  
Intersection Numbers ◽  
Moduli Spaces Of Curves

scholarly journals Masur–Veech volumes, frequencies of simple closed geodesics, and intersection numbers of moduli spaces of curves

2021 ◽  
Vol -1 (-1) ◽  
Author(s):  
Vincent Delecroix ◽  
Élise Goujard ◽  
Peter Zograf ◽  
Anton Zorich
Keyword(s):  
Moduli Spaces ◽  
Closed Geodesics ◽  
Intersection Numbers ◽  
Moduli Spaces Of Curves ◽  
Simple Closed Geodesics

Recursions and asymptotics of intersection numbers

2016 ◽  
Vol 27 (09) ◽  
pp. 1650072 ◽  
Author(s):  
Kefeng Liu ◽  
Motohico Mulase ◽  
Hao Xu
Keyword(s):  
Asymptotic Expansion ◽  
Moduli Spaces ◽  
Painlevé Equation ◽  
Intersection Numbers ◽  
Asymptotics Of Solutions ◽  
Moduli Spaces Of Curves ◽  
Large Genus ◽  
Painleve Equation

We establish the asymptotic expansion of certain integrals of [Formula: see text] classes on moduli spaces of curves [Formula: see text], when either the [Formula: see text] or [Formula: see text] goes to infinity. Our main tools are cut-join type recursion formulae from the Witten–Kontsevich theorem, as well as asymptotics of solutions to the first Painlevé equation. We also raise a conjecture on large genus asymptotics for [Formula: see text]-point functions of [Formula: see text] classes and partially verify the positivity of coefficients in generalized Mirzakhani’s formula of higher Weil–Petersson volumes.

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