2022: Dr Matthew Conder, the University of Auckland, has been awarded a Rutherford Foundation Postdoctoral Fellowship for research titled: ‘Algorithms for p-adic linear groups’
In mathematics, a 'group' is an abstract algebraic structure used to model and analyse the symmetries of an object, and a linear group is a group consisting of matrices. Linear groups have played a central role in mathematics for almost 200 years through their role in computation, acting as an important bridge between formal mathematics and the physical sciences. They can be used to power a diverse range of real-world applications in fields such as medical imaging, robotics and crystallography. Algorithms are used to identify and solve challenging fundamental problems for certain linear groups, but more work is needed to develop more- effective and efficient algorithms.
In his Rutherford Postdoctoral Fellowship Dr Matthew Conder will explore a specific class of linear groups, p-adic linear groups, which have a variety of applications in geometry, number theory and physics. He will develop novel algorithms and use them to investigate and to solve challenging problems for certain p-adic linear groups. Dr Conder hopes that, by developing new connections between aspects of algebra and geometry, he will make significant advances in computational and geometric group theory.
Dr Conder believes this project will lead to key developments in fundamental areas of mathematics which underpin a variety of important applications in computer science, data science and cryptography. In particular, investigating Bruhat-Tits trees (pictured), which are combinatorial structures with deep connections to post-quantum cryptography, error-correcting codes and neural networks. Finally, Dr Conder also aims to develop a research hub in Aotearoa for geometric group theory – a dynamic field of mathematics.