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 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.
• 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 Thomas works on geometric group theory and the topics of lattices, rigidity and buildings.
• Dr Zhang works on nonlinear partial differential equations coming from differential geometry consideration (for example, Ricci flow and the complex version of it).

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, surface theory, spectral curves, integrable systems, geometric evolution equations, pluripotential theory, geometric group theory.

Contact Person

Dr L. Paunescu (laurentiu.paunescu@sydney.edu.au)