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Research

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)