Dr Vitalijs Brejevs

Project Title: Cobordism in smooth and symplectic topology

My PhD project is titled “Cobordism in smooth and symplectic topology” and is concerned with topology and geometry in dimension at most four, specifically, with the study of knots (tangled loops in 3-dimensional space) and contact/symplectic structures (constructions that help understand certain 3- and 4-dimensional spaces). The aims of the project are twofold, namely to confirm the so-called ‘slice-ribbon’ conjecture, which gives conditions for how some knots can be boundaries of discs, for a particular class of knots, and to attempt an ambitious task of classifying possible contact/symplectic structures.