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Gromov–Witten invariants of ℙ1 and Eynard–Orantin invariants

- P. Norbury, Nick Scott
- Mathematics
- 7 June 2011

We prove that stationary Gromov-Witten invariants of $\bp^1$ arise as the Eynard-Orantin invariants of the spectral curve $x=z+1/z$, $y=\ln{z}$. As an application we show that tautological… Expand

Weil–Petersson volumes and cone surfaces

- Norman Do, P. Norbury
- Mathematics
- 16 March 2006

The moduli spaces of hyperbolic surfaces of genus g with n geodesic boundary components are naturally symplectic manifolds. Mirzakhani proved that their volumes are polynomials in the lengths of the… Expand

A new cohomology class on the moduli space of curves

- P. Norbury
- Mathematics
- 11 December 2017

We define a collection of cohomology classes $\Theta_{g,n}\in H^{4g-4+2n}(\overline{\cal M}_{g,n})$ for $2g-2+n>0$ that restrict naturally to boundary divisors. We prove that a generating function… Expand

Quantum spectral curve for the Gromov-Witten theory of the complex projective line

- P. Dunin-Barkowski, M. Mulase, P. Norbury, A. Popolitov, S. Shadrin
- Mathematics, Physics
- 18 December 2013

We construct the quantum curve for the Gromov-Witten theory of the complex projective line.

Counting lattice points in the moduli space of curves

- P. Norbury
- Mathematics
- 30 January 2008

We show how to define and count lattice points in the moduli space $\modm_{g,n}$ of genus $g$ curves with $n$ labeled points. This produces a polynomial with coefficients that include the Euler… Expand

String and dilaton equations for counting lattice points in the moduli space of curves

- P. Norbury
- Mathematics
- 26 May 2009

We prove that the Eynard-Orantin symplectic invariants of the curve xy-y^2=1 are the orbifold Euler characteristics of the moduli spaces of genus g curves. We do this by associating to the… Expand

Simple geodesics and Markoff quads

- Yi Huang, P. Norbury
- Mathematics
- 26 December 2013

The action of the mapping class group of the thrice-punctured projective plane on its $$\mathop {\mathrm{GL}}\nolimits (2,{\mathbb {C}})$$GL(2,C) character variety produces an algorithm for… Expand

DUBROVIN’S SUPERPOTENTIAL AS A GLOBAL SPECTRAL CURVE

- P. Dunin-Barkowski, P. Norbury, N. Orantin, A. Popolitov, S. Shadrin
- MathematicsJournal of the Institute of Mathematics of…
- 23 September 2015

We apply the spectral curve topological recursion to Dubrovin’s universal Landau–Ginzburg superpotential associated to a semi-simple point of any conformal Frobenius manifold. We show that under some… Expand

QUANTUM CURVES AND TOPOLOGICAL RECURSION

- P. Norbury
- Mathematics, Physics
- 16 February 2015

This is a survey article describing the relationship between quantum curves and topological recursion. A quantum curve is a Schroperator-like noncommutative analogue of a plane curve which encodes… Expand

Spectral Curves and the Mass of Hyperbolic Monopoles

- P. Norbury, N. M. Romão
- Mathematics
- 23 December 2005

The moduli spaces of hyperbolic monopoles are naturally fibred by the monopole mass, and this leads to a nontrivial mass dependence of the holomorphic data (spectral curves, rational maps,… Expand

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