Applied Algebra and Information Theory

Applied Algebra and Information Theory

in digital communications and storage technology are driven by a range of fundamental areas in algebra and discrete mathematics. The focus of the Applied Algebra Group in UCD is in core topics in algebra with applications to coding, cryptography and computation. We have published widely in topics such as combinatorics over finite rings and fields, algebraic coding theory, coding, graphs & designs,  the Discrete Log Problem, elliptic curve cryptography, network coding, APN functions, S-boxes in symmetric cryptosystems, Gröbner bases, finite geometry, number theory, group representations and applications to quantum computing. Beyond this, have strong interests in the application of discrete structures and methods in physics, chemistry, and life sciences.

People

Assoc Prof Eimear Byrne
Research Interests: Discrete mathematics, combinatorics, algebraic coding theory, tensors, algebra in communications

(opens in a new window)Assoc Prof Marcus Greferath
Research Interests: Discrete mathematics, abstract algebra, geometry, computer science

Assoc Prof Russell Higgs (Emeritus)
Research Interests: Representation Theory, Coding Theory, Wireless Sensor Network

Dr Rupert Levene
Research Interests: Functional Analysis, Operator Algebras, Operator Spaces, Quantum Information Theory

Prof Gary McGuire
Research Interests: Finite Mathematics, Coding, Cryptography, Computation, Algebraic Number Theory, Algebraic Geometry

Dr John Sheekey
Research Interests: Semifields, Nonassociative Algebras, Rank-Metric Coding, Random Network Coding, Tensors

Group Contact (Email): (opens in a new window)Assoc Professor Eimear Byrne