Paul Norbury's Papers
Weil-Petersson volumes, stability conditions and wall-crossing
Joint with Lukas Anagnostou and Scott Mullane.
Volumes of moduli spaces of hyperbolic surfaces with cone points
Joint with Lukas Anagnostou
Polynomial relations among kappa classes on the moduli space of curves.
Joint with Maxim Kazarian
To appear IMRN.
An intersection-theoretic proof of the Harer-Zagier formula.
Joint with Alessandro Giacchetto and Danilo Lewanski
Algebraic Geometry 10 (2023), 130-147.
Airy structures and deformations of curves in surfaces.
Joint with Wee Chaimanowong, Michael Swaddle and Mehdi Tavakol
Enumerative geometry via the moduli space of super Riemann surfaces
JNR monopoles.
Joint with Michael Murray
Quart. J. Math. 72 (2021), 387-405.
Loop equations for Gromov-Witten invariants of P1.
Joint with Gaëtan Borot
SIGMA 15 (2019), 061, 29 pages.
Gromov-Witten invariants of P1 coupled to a KdV tau function.
Adv. Math. 399 (2022), 108227.
A new cohomology class on the moduli space of curves
To appear Geom. Topol.
Topological recursion with hard edges
Joint with Leonid Chekhov
Inter. Journal Math. 30, No. 3 (2019) 1950014 (29 pages).
Topological recursion on the Bessel curve
Joint with Norman Do
Comm. Number Theory and Physics 12 (2018), 53-73.
Primary invariants of Hurwitz Frobenius manifolds
Joint with Dunin-Barkowski, Orantin, Popolitov and Shadrin.
Topological Recursion and its influence in Analysis, Geometry and Physics, Proceedings of Symposia in Pure Mathematics 100 (2018), 297-332.
Dubrovin's superpotential as a global spectral curve.
Joint with Dunin-Barkowski, Orantin, Popolitov and Shadrin.
J. Inst. Math. Jussieu 18 (2019), 449-497.
Topological recursion for Gaussian means and cohomological field theories.
Joint with Jørgen Andersen, Leonid Chekhov and Robert Penner.
Theor. Math. Phys. 185 (3) (2015), 1685-1717.
Quantum curves and topological recursion.
Proceedings of Symposia in Pure Mathematics, String-Math 2014 93 (2016), p.41-65.
Models of discretized moduli spaces, cohomological field theories, and Gaussian means.
Joint with Jørgen Andersen, Leonid Chekhov and Robert Penner.
Journal of Geometry and Physics 98 (2015), 312-329.
Topological recursion for irregular spectral curves.
Joint with Norman Do
Journal of the London Mathematical Society 97 (2018), 398-426.
Pruned Hurwitz numbers.
Joint with Norman Do
Transactions of the AMS 370 (2018), 3053-3084.
Simple geodesics and Markoff quads.
Joint with Yi Huang
Geometriae Dedicata 186 (2017), 113-148.
Quantum spectral curve for the Gromov-Witten theory of the complex projective line.
Joint with Dunin-Barkowski, Mulase, Popolitov and Shadrin
Journal für die reine und angewandte Mathematik 726 (2017), 267-290.
Orbifold Hurwitz numbers and Eynard-Orantin invariants.
Joint with Norman Do and Oliver Leigh
Math. Res. Lett. 23 (2016), 1281-1327.
Stationary Gromov-Witten invariants of projective spaces.
Acta Mathematica Sinica 33 (2017), 1163-1183.
Gromov-Witten invariants of P1 and Eynard-Orantin invariants.
Joint with Nick Scott
Geometry & Topology 18 (2014), 1865-1910.
Cell decompositions of moduli space, lattice points and Hurwitz problems.
Handbook of Moduli. Advanced Lectures in Mathematics 24 (2013), Volume III, 39-74.
Polynomials representing Eynard-Orantin invariants.
Joint with Nick Scott
Quart. J. Math. 64 (2013), 515-546.
String and dilaton equations for counting lattice points in the moduli space of curves.
Transactions AMS. 365 (2013), 1687-1709.
arXiv:0905.4141 [math.AG]
Morse field theory
Joint with Ralph Cohen.
Asian Journal of Math. 16 (2012) No. 4, 661-712.
Counting lattice points in compactified moduli spaces of curves.
Joint with Norman Do
Geometry & Topology 15 (2011), 2321-2350.
Magnetic monopoles on manifolds with boundary.
Transactions AMS 363 (2011), 1287-1309.
arXiv:0804.3649 [math.DG]
Counting lattice points in the moduli space of curves.
Math. Res. Lett. 17 (2010), 467-481.
arXiv:0801.4590 [math.AG]
Weil-Petersson volumes and cone surfaces
Joint with Norman Do
Geometriae Dedicata 141 (2009), 93-107.
Lengths of geodesics on non-orientable hyperbolic surfaces
Geometriae Dedicata 134 (2008), 153-176.
Stable reduction and topological invariants of complex polynomials
Real and Complex Singularities, Proceedings of the Australian-Japanese Workshop, University of Sydney, Australia 5-8 Sept 2005. Editors Paunescu et al. (2007), 299-322.
Spectral curves and the mass of hyperbolic monopoles
Joint with Nuno Romao.
Communications in Mathematical Physics 270 (2007), 295-333.
Closed geodesics on incomplete surfaces.
Joint with J. Hyam Rubinstein.
Geometriae Dedicata 116 (2005), 1-36.
Algebraic Analysis of Linear Precoding for Blind Channel
Joint with Manton, J. H. and Neumann, W. D.
Systems and Control Letters. 54 (2005),125-134
Boundary algebras of hyperbolic monopoles
Journal of Geometry and Physics. 51 (2004), 13-33.
Minimal spheres of arbitrarily high Morse index
Joint with Joel Hass and J. Hyam Rubinstein.
Communications in Analysis and Geometry. 11 (2003), p.425-439.
Hyperbolic monopoles and holomorphic spheres
Joint with Michael Murray and Michael Singer.
Annals of Global Analysis and Geometry 23 (2003), 101-128.
The Orevkov invariant of an affine plane curve
Joint with Walter Neumann.
Transactions of the AMS 355 (2003), 519-538.
Rational polynomials of simple type
Joint with Walter Neumann.
Pacific Journal of Mathematics. 204 (2002), 177-207.
A proof of Atiyah's conjecture on configurations of four points in
Euclidean three-space.
Joint with Michael Eastwood.
Geometry & Topology 5 (2001), 885-893.
Asymptotic values of hyperbolic monopoles
Journal of the LMS 64 (2001), 245-256.
Unfolding polynomial maps at infinity
Joint with Walter Neumann.
Mathematische Annalen 318 (2000), 149-180.
Periodic instantons and the loop group
Communications in Mathematical Physics. 212 (2000), 557-569.
Vanishing cycles and monodromy of complex polynomials
Joint with Walter Neumann.
Duke Math. J. 101 (2000), 487-497.
Global Identifiability of Channel Identification Problems
Joint with Manton, J. H. and Neumann, W. D. and Hua, Y.
Proceedings of the Second International Conference on Information,
Communications and Signal Processing, Dec. (1999), Singapore.
Nontrivial rational polynomials in two variables have reducible fibres
Joint with Walter Neumann.
Bull. Australian Maths Society 58 (1998), 501-503.
Degenerating metrics and instantons on the four-sphere
Joint with Stuart Jarvis.
J. Geometry and Physics 27 (1998), 79-98.
Compactification of hyperbolic monopoles
Joint with Stuart Jarvis.
Nonlinearity 10 (1997), 1073-1092.
Zero and infinite curvature limits of hyperbolic monopoles
Joint with Stuart Jarvis.
Bulletin of the LMS 29 (1997), 737-744.
Real instantons and quaternionic classifying spaces
Joint with Marc Sanders.
Proceedings of the AMS 124 (1996)