Norbury's Home Page

Australia 3010.

Office: 170

Email: pnorburyATms.unimelb.edu.au

Phone: +61 3 83447163 Fax: +61 3 83444599

Courses Semester 2, 2008:

Linear Algebra
Complex Analysis

Research

My research interests are in geometry, particularly problems motivated from mathematical physics. A common theme to my research is different moduli space problems. My most recent papers are Magnetic monopoles on manifolds with boundary which proves that for given holomorphic information, a Hecke modification of a holomorphic bundle over a Riemann surface, there exists a unique solution to the Bogomolny equation, a magnetic monopole, on the product of the interval with the surface and a Riemannian metric on that surface. This result confirms geometric invariant theory ideas - that a symplectic quotient equals a complex quotient - of Kapustin and Witten. Counting lattice points in the moduli space of curves defines and counts lattice points in the moduli space of curves. The lattice points correspond to curves defined over the algebraic numbers. The count yields information about the moduli space such as its Euler characteristic and intersection numbers. Lengths of geodesics on non-orientable hyperbolic surfaces gives a McShane identity for lengths of geodesics on non-orientable hyperbolic surfaces. Weil-Petersson volumes and cone surfaces describes relations between volumes of moduli spaces of hyperbolic surfaces, and is joint with Norman Do. See my research interests and papers in the side menu for more.