Number Theory
Research Groups
- Actuarial and Financial Mathematics
- Applied Algebra and Information Theory
- Bayesian Statistics
- Computational Mathematics and High-Performance Computing
- Enumerative Combinatorics
- Fluid Dynamics
- Functional Analysis
- Mathematics Education
- Matrix Analysis
- Number Theory
- Potential Theory
- Probability
- Quantum Information and Computation
- Real Algebra
- Relativity and Mathematical Physics
- Statistical Genetics and Bioinformatics
- Statistical Modelling
Number Theory
Number Theory is one of the oldest and most vibrant branches of mathematics. It is unique in that it combines problems and easily formulated questions with truly deep and technical methods for addressing these questions. For example, Wiles’ spectacular proof of Fermat’s Last Theorem in 1994 incorporated many powerful techniques which have enriched the whole of mathematics.
The Number Theory Group at UCD has expertise in the arithmetic aspects of the (opens in a new window)Langlands Programme ((opens in a new window)Kazim Büyükboduk), homology theory of special linear groups (Kevin Hutchinson) and q-series and modular forms (Robert Osburn). Our goal is to make UCD an international centre of excellence in this research area
Number theory possesses an accessibility and applicability, both of which are characteristics of a subject which must play a central role for the future of mathematics in Ireland.
Number theory has enjoyed a long and fruitful interaction with many other areas in mathematics. For example, many number theoretic constructions find an application in cryptography, coding theory, and internet security. Elliptic curve cryptography, the Diffie-Hellman protocal via class groups, integer factorization, and RSA signature schemes are some examples of recent developments. Moreover, multinational technological companies in Ireland such as Zynga, Quest, HCL, Google, Intel, Amgen, Facebook and Dropbox benefit from interactions with Ph.D. graduates, postdocs and faculty in number theory.
People
(opens in a new window)Dr Kazim Buyukboduk
Research Interests: Algebraic Number Theory, Iwasawa theory of automorphic motives and their deformations, Euler systems.
Dr Kevin Hutchinson
Research Interests: Algebraic K-theory, Homological Algebra, Number Theory
Dr Robert Osburn
Research Interests: Number Theory, Q-Series, Modular Forms
Group Contact (Email): (opens in a new window)Dr Kazim Buyukboduk