# Number Theory

## Research Interests of the Number Theory Group

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;

## Research Areas

Algebraic and analytic number theory, arithmetic geometry, and cryptography.

## Contact Person

Dr Adrian Nelson (A.Nelson@maths.usyd.edu.au)