###Symmetry and structure in pure mathematics
Project ID: 2228bd1197 (You will need this ID for your application)
Research Theme: Mathematical Sciences
UCL Lead department: Mathematics
Lead Supervisor: Yiannis Petridis
Project Summary:
Pure mathematics is the study of abstract structures, questions of symmetry, shape, number, and limits. Research in pure mathematics is generally pursued for its own sake, but our progress underpins developments in applied mathematics and ultimately all of science and engineering.
This project will push forward the boundaries of the field, using cutting edge techniques drawn from parts of geometry, algebra, number theory, analysis, and combinatorics. Depending on the background and interests of the student, potential areas of investigation include automorphic forms, Shimura varieties, gauge theory, extremal graph theory, dynamical systems, Ramsey theory, derived categories, microlocal analysis, and spectral theory.
The initial period of the project will begin with reviews of the literature and developing your knowledge of necessary specialist techniques. You will then move into research, formulating your own conjectures and proving your own original results.
Applicants should have a strong background in pure mathematics at a Masters level and be able to demonstrate a passion for the subject and in-depth knowledge of at least one subfield. You will be supervised by Prof. Yiannis Petridis, with other members of the department potentially involved as part of the supervisory team.