Level: MSci
Title: Definable sets over finite fields
Supervisor:

Dr Ivan Tomasic
Research Area: Geometry and Analysis
Description:

This project is aimed at a student with interests not only in algebraic geometry and number theory, but also in logic. A typical formula over finite fields is of form \varphi(\bar{x})~\equiv ~\exists y ~p( \bar{x}, y) = 0, where \bar{x} = x_1 \ldots x_r and p(\bar{x},y) is a polynomial in r+1 variables over the prime field \mathbb{F}_p. One is then interested, for each n \in \mathbb{N}, in counting the number N_n of r-tuples \bar{x} from \mathbb{F}_{p^n} satisfying the formula \phi. For further details of the project see this document.
Further Reading:
Key Modules:

To be confirmed with supervisor.
Other Information:
Current Availability: Yes