Number Theory

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)