- School of Mathematics and Statistics - Research Publications
School of Mathematics and Statistics - Research Publications
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ItemNo Preview AvailableAn intersection-theoretic proof of the Harer-Zagier formulaGiacchetto, A ; Lewanski, D ; Norbury, P (EUROPEAN MATHEMATICAL SOC-EMS, 2023-03)
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ItemNo Preview AvailablePolynomial Relations Among Kappa Classes on the Moduli Space of CurvesKazarian, M ; Norbury, P (OXFORD UNIV PRESS, 2024-02-07)Abstract We construct an infinite collection of universal—independent of $(g,n)$—polynomials in the Miller–Morita–Mumford classes $\kappa _m\in H^{2m}( \overline{\mathcal{M}}_{g,n},{\mathbb{Q}})$, defined over the moduli space of genus $g$ stable curves with $n$ labeled points. We conjecture vanishing of these polynomials in a range depending on $g$ and $n$.
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ItemNo Preview AvailableGromov-Witten invariants of P 1 coupled to a KdV tau functionNorbury, P (ACADEMIC PRESS INC ELSEVIER SCIENCE, 2022-04-16)
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ItemTopological recursion for irregular spectral curvesDo, N ; Norbury, P (WILEY, 2018-06)
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ItemSimple geodesics and Markoff quadsHuang, Y ; Norbury, P (Springer, 2017-02-01)The action of the mapping class group of the thrice-punctured projective plane on its GL(2,C) character variety produces an algorithm for generating the simple length spectra of quasi-Fuchsian thrice-punctured projective planes. We apply this algorithm to quasi-Fuchsian representations of the corresponding fundamental group to prove: a sharp upper-bound for the length its shortest geodesic, a McShane identity and the surprising result of non-polynomial growth for the number of simple closed geodesic lengths.
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ItemCOUNTING LATTICE POINTS IN THE MODULI SPACE OF CURVESNorbury, P (INT PRESS BOSTON, INC, 2010-05)
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ItemWeil-Petersson volumes and cone surfacesDo, N ; Norbury, P (SPRINGER, 2009-08)
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ItemSpectral curves and the mass of hyperbolic monopolesNORBURY, P. ; ROMAO, N. ( 2007)
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ItemThe Orevkov invariant of an affine plane curveNeumann, WD ; Norbury, P (AMER MATHEMATICAL SOC, 2003)
We show that although the fundamental group of the complement of an algebraic affine plane curve is not easy to compute, it possesses a more accessible quotient, which we call the Orevkov invariant.
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ItemMinimal spheres of arbitrarily high morse indexHASS, J. ; NORBURY, P. T. ; RUBINSTEIN, J. H. ( 2003)