Norbury's Papers

**Paul Norbury's Papers**
Combinatorics and large genus asymptotics of the Brézin-Gross-Witten numbers Joint with Jindong Guo, Di Yang and Don Zagier	arXiv:2412.20388
Super volumes and KdV tau functions Joint with Alexander Alexandrov	arXiv:2412.17272
Super Weil-Petersson measures on the moduli space of curves	arXiv:2312.14558
Weil-Petersson volumes, stability conditions and wall-crossing Joint with Lukas Anagnostou and Scott Mullane.	arXiv:2310.13281
Volumes of moduli spaces of hyperbolic surfaces with cone points Joint with Lukas Anagnostou	arXiv:2212.13701
Polynomial relations among kappa classes on the moduli space of curves. Joint with Maxim Kazarian IMRN 3 (2024), 1825-1867.	arXiv:2112.11672
An intersection-theoretic proof of the Harer-Zagier formula. Joint with Alessandro Giacchetto and Danilo Lewanski Algebraic Geometry 10 (2023), 130-147.	arXiv:2112.11137
Airy structures and deformations of curves in surfaces. Joint with Wee Chaimanowong, Michael Swaddle and Mehdi Tavakol J. London Math. Soc. 109 (2023).	arXiv:2012.00254
Enumerative geometry via the moduli space of super Riemann surfaces	arXiv:2005.04378
JNR monopoles. Joint with Michael Murray Quart. J. Math. 72 (2021), 387-405.	arXiv:1912.05718
Loop equations for Gromov-Witten invariants of P¹. Joint with Gaëtan Borot SIGMA 15 (2019), 061, 29 pages.	arXiv:1905.01890
Gromov-Witten invariants of P¹ coupled to a KdV tau function. Adv. Math. 399 (2022), 108227.	arXiv:1812.04221
A new cohomology class on the moduli space of curves Geom. Top. 27 (2023), 2695-2761.	arXiv:1712.03662
Topological recursion with hard edges Joint with Leonid Chekhov Inter. Journal Math. 30, No. 3 (2019) 1950014 (29 pages).	arXiv:1702.08631
Topological recursion on the Bessel curve Joint with Norman Do Comm. Number Theory and Physics 12 (2018), 53-73.	arXiv:1608.02781
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.	arXiv:1605.07644
Dubrovin's superpotential as a global spectral curve. Joint with Dunin-Barkowski, Orantin, Popolitov and Shadrin. J. Inst. Math. Jussieu 18 (2019), 449-497.	arXiv:1509.06954
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.	arXiv:1512.09309
Quantum curves and topological recursion. Proceedings of Symposia in Pure Mathematics, String-Math 2014 93 (2016), p.41-65.	arXiv:1502.04394
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.	arXiv:1501.05867
Topological recursion for irregular spectral curves. Joint with Norman Do Journal of the London Mathematical Society 97 (2018), 398-426.	arXiv:1412.8334
Pruned Hurwitz numbers. Joint with Norman Do Transactions of the AMS 370 (2018), 3053-3084.	arXiv:1312.7516
Simple geodesics and Markoff quads. Joint with Yi Huang Geometriae Dedicata 186 (2017), 113-148.	arXiv:1312.7089
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.	arXiv:1312.5336
Orbifold Hurwitz numbers and Eynard-Orantin invariants. Joint with Norman Do and Oliver Leigh Math. Res. Lett. 23 (2016), 1281-1327.	arXiv:1212.6850
Stationary Gromov-Witten invariants of projective spaces. Acta Mathematica Sinica 33 (2017), 1163-1183.	arXiv:1112.6400
Gromov-Witten invariants of P¹ and Eynard-Orantin invariants. Joint with Nick Scott Geometry & Topology 18 (2014), 1865-1910.	arXiv:1106.1337
Cell decompositions of moduli space, lattice points and Hurwitz problems. Handbook of Moduli. Advanced Lectures in Mathematics 24 (2013), Volume III, 39-74.	arXiv:1006.1153
Polynomials representing Eynard-Orantin invariants. Joint with Nick Scott Quart. J. Math. 64 (2013), 515-546.	arXiv:1001.0449
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.	math.GT/0509681
Counting lattice points in compactified moduli spaces of curves. Joint with Norman Do Geometry & Topology 15 (2011), 2321-2350.	arXiv:1012.5923
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.	math.AG/0603406
Lengths of geodesics on non-orientable hyperbolic surfaces Geometriae Dedicata 134 (2008), 153-176.	math.GT/0612128
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.	math.AG/0605267
Spectral curves and the mass of hyperbolic monopoles Joint with Nuno Romao. Communications in Mathematical Physics 270 (2007), 295-333.	math-ph/0512083
Closed geodesics on incomplete surfaces. Joint with J. Hyam Rubinstein. Geometriae Dedicata 116 (2005), 1-36.	math.GT/0309159
Algebraic Analysis of Linear Precoding for Blind Channel Identification 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.	math-ph/0106013
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.	math.GT/0206286
Hyperbolic monopoles and holomorphic spheres Joint with Michael Murray and Michael Singer. Annals of Global Analysis and Geometry 23 (2003), 101-128.	math.DG/0111202
The Orevkov invariant of an affine plane curve Joint with Walter Neumann. Transactions of the AMS 355 (2003), 519-538.	math.AG/0110286
Rational polynomials of simple type Joint with Walter Neumann. Pacific Journal of Mathematics. 204 (2002), 177-207.	math.AG/0008080
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.	math.MG/0109161
Asymptotic values of hyperbolic monopoles Journal of the LMS 64 (2001), 245-256.	math.DG/9911146
Unfolding polynomial maps at infinity Joint with Walter Neumann. Mathematische Annalen 318 (2000), 149-180.	math.AG/9910054
Periodic instantons and the loop group Communications in Mathematical Physics. 212 (2000), 557-569.	math-ph/9902007
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.	math.AG/9805093
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)