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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

Teaching

Semester 2, 2024:

Research

My research interests are in geometry, particularly problems motivated from mathematical physics. A common theme to my research involves various moduli space problems. My most recent papers are
A family of finite measures on the moduli space of curves and super volumes
which defines a family of finite measures on the moduli space of smooth curves with marked points. The measures are defined via a construction analogous to that of the Weil-Petersson metric using the extra data of a spin structure.
Weil-Petersson volumes, stability conditions and wall-crossing
which is joint with Lukas Anagnostou and Scott Mullane, where we prove a wall-crossing formula for volumes of moduli spaces of hyperbolic surfaces with cone angles.
Volumes of moduli spaces of hyperbolic surfaces with cone points
which is joint with Lukas Anagnostou, where we calculate some new volumes of moduli spaces of hyperbolic surfaces with cone angles.
Polynomial relations among kappa classes on the moduli space of curves
which is joint with Maxim Kazarian, where we construct a collection of polynomials in kappa classes on the moduli space of stable curves which conjecturally vanish, and would give new relations in the Chow ring.
An intersection-theoretic proof of the Harer-Zagier formula
which is joint with Alessandro Giacchetto and Danilo Lewanski, where we prove a formula for the Euler characteristic of the moduli space of smooth curves in terms of Hodge integrals. See my research interests and papers in the side menu for more.