Topics in Number Theory

Project ID: 2228cd1408 (You will need this ID for your application)

Under Offer

Research Theme: Mathematical Sciences

UCL Lead department: Mathematics

Department Website

Lead Supervisor: Yiannis Petridis

Project Summary:

The proposed research will investigate aspects of algebraic and analytic number theory, and arithmetic geometry. Some computational methods may be involved. Potential directions include:

• the arithmetic of elliptic curves and of Jacobians of higher genus curves, and the Birch-Swinnerton-Dyer conjecture.

• the analytic theory of L-functions and automorphic forms.

• the arithmetic and cohomology of locally symmetric spaces.

• the p-adic Langlands programme, especially the cohomology of arithmetic groups and their p-adic Banach space representations.

• Shimura varieties and the Andre-Oort conjecture.