Geometry and Topology

Research Interests of the Geometry and Topology Group

Geometry and Topology study the global structure of the sets of solutions of systems of equations, considered as higher dimensional analogues of curves and surfaces in space.

Dr Hillman is working on the algebraic topology of low-dimensional manifolds, and in particular is interested in the influence of Poincaré duality on the fundamental group. Dr Kuo and Dr Paunescu are working on singularity theory and algebraic geometry over the classical fields. Dr Carberry works on geometric aspects of integrable systems, in particular the role that integrable systems play in allowing one to apply techniques from algebraic geometry to differential-geometric problems.

Research Areas

Algebraic invariants of 4-manifolds, knot theory, homological group theory, real and complex singularities, stratifications and subanalytic sets, Hodge theory, topology of algebraic varieties, integrable systems, surface theory, spectral curves.

Contact Person

Dr J. A. Hillman (J.Hillman@maths.usyd.edu.au)