Algebra and structures

A key role of modern mathematics is to detect and analyse structures in a broad range of domains, from particle physic to cosmology, from data sets to neural networks.

New insights and predictions are often only made possible from a deep understanding of an abstract theoretical framework, and uncover structure where chaos seemed to reign.

The interaction of algebra—one of the oldest structure theories—with diverse areas within and outside of mathematics leads to the formulation and discovery of new algebraic structures.

Other structure theories analysed and employed by the group at the University of Sydney in order to uncover secrets about the formation and role of structure in a broad range of phenomena include dynamical and integrable systems, networks and complex systems.

Header image: Anne Thomas: “Folded Galleries in an affine building”

Research areas

• 
Integrable Systems

  
• Networks and complex systems

• Group theory and generalisations

• Representation theory

• Number Theory

• Combinatorics

• Dynamical Systems and Ergodic Theory
• 
Lie theory

• Computational Algebra (MAGMA)