Paul Norbury's home page

School of Mathematics and
Statistics
 University of Melbourne
 Australia 3010.
 Office: 170
 Email: norburyATunimelb.edu.au
 Phone: +61 3 83447163 Fax: +61 3 83444599
Research
My research interests are in geometry, particularly problems
motivated from mathematical physics. A common theme to my research is
various moduli space problems. My most recent papers are
A new cohomology class on the moduli space of curves.
where we construct a cohomology class on the moduli space of curves which naturallu pairs with any cohomological field theory.
Topological recursion with hard edges.
joint with Leonid Chekhov where we prove a Givental type decomposition for partition functions that arise out of topological recursion into products of KonstevichWitten and BrezinGrossWitten KdV tau functions.
Topological recursion on the Bessel curve.
joint with Norman Do where we describe an analogue of the Airy curve which describes local irregular behaviour of spectral curves.
Primary invariants of Hurwitz Frobenius manifolds.
joint with DuninBarkowski, Orantin, Popolitov, Shadrin where we obtain the primary invariants of a Hurwitz Frobenius manifold via periods of a differential along cycles on the domain curve, generalising the construction of flat coordinates via periods.
Dubrovin's superpotential as a global spectral curve.
joint with DuninBarkowski, Orantin, Popolitov, Shadrin where we apply topological recursion to a spectral curve produced from any conformal Frobenius manifold
via a construction of Dubrovin.
Topological recursion for Gaussian means and cohomological field theories.
joint with Jørgen Andersen, Leonid Chekhov and Robert Penner
which proves integrality results for coefficients coming out of the Hermitian matrix model.
Quantum curves and topological recursion.
which is a survey article on quantum curves.
See my research interests and papers in the side menu for more.