CARMA Research Group
Number Theory, Algorithms and Discrete Mathematics
Leader: Ljiljana Brankovic and Richard Brent
This group covers a wide range of research interests from number theory, combinatorics and theoretical computer science, and in particular the interplay between these fields as well as links to analysis and algebraic geometry.
Topics of interest include: Diophantine analysis and Mahler functions; the arithmetic of global fields including elliptic curves, Drinfeld modules and associated modular forms; special integer sequences and special values of analytic functions; Hadamard matrices; combinatorics, enumeration and the probabilistic method; graph theory, optimal networks and other discrete structures.
There is a strong focus on computational aspects of such topics, including experimental mathematics, visualisation, computational number theory and the analysis of algorithms.
Potential applications of our work range from coding theory and cryptography through group theory, counting points on algebraic varieties to computer networks and even theoretical physics.
Members of this research group:
- Brian Alspach
- David Bailey
- Ljiljana Brankovic
- Richard Brent
- Florian Breuer
- Stephan Chalup
- Tony Guttman
- Yuqing Lin
- Jim MacDougall
- Andrew Mattingly
- Judy-anne Osborn
- Joe Ryan
- Matt Skerrit