Algebraic, analytic, and arithmetic geometric aspects of number theory.
- Arithmetic geometry:
- Arithmetic of curves, abelian varieties and their moduli, Shimura varieties;
- Classical modular forms and functions;
- p-adic Hodge theory, p-adic modular forms;
- Algebraic number theory:
- Class field theory;
- Quadratic forms, quaternions, and noncommutative algebras;
- Galois representations, deformation theory;
- Algorithmic and computational number theory:
- Explicit algorithms, computational complexity, and effective methods in number theory.
- Cryptographic applications;
- Analytic number theory:
- Spectral theory of group actions on discrete structures such as graphs, trees, and buildings;
- Automorphic forms, automorphic representations and L-functions;
Algebraic and analytic number theory, arithmetic geometry, and cryptography.
Dr Adrian Nelson (A.Nelson@maths.usyd.edu.au)