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Inside view of the Seifert-Weber Space by Jeff Weeks

Geometry and topology

New insights about the shapes and structures of spaces
The nexus of diverse research areas such as algebraic geometry, differential geometry, and complex systems.

The study of geometry has its roots in ancient times. Topology, the mathematical study of the shape of spaces, has its origins in the nineteenth century. Today, geometry and topology are intertwined thriving fields of research that offer new insights into many different branches of mathematics and theoretical physics.

At their nexus, these areas meet and develop a synergy, they are influenced by geometry and topology, and enrich geometry and topology. Such interaction between work in geometry and topology and neighbouring areas is also true of the group at the University of Sydney.

Header image: Inside view of the Weber-Seifert Space, produced with Curved Spaces by Jeff Weeks

Research areas

  • Differential Geometry
  • Algebraic Topology
  • Algebraic Geometry
  • Networks and complex systems
  • Lie theory
  • Mathematical Physics