Finlay is working in Harmonic Analysis under the supervisor of Prof. Anthony Carbery, with a particular interest in Geometric inequalities and Multilinear Harmonic Analysis. Finlay is also interested in the applications of the polynomial method in Harmonic Analysis.
He holds a BSc from the University of Edinburgh, where he explored a wide range of areas in Pure Mathematics. During his undergraduate, he worked on a project developing a proof of Invariance of Domain Theorem using purely tools from Real Analysis. Finlay chose to explore the area of Algebraic Geometry for his dissertation and worked on the proof of Max Noether's Theorem, the geometrical approach of which he particularly enjoyed.