Dr Stephen Lynch is a Lecturer in Pure Mathematics in the Department of Mathematics, at King’s College London.

Dr Stephen Lynch is a Lecturer in Pure Mathematics at King’s. He studied at the University of Queensland and Free University of Berlin before obtaining a PhD at the University of Tuebingen. He then joined Imperial College as a Chapman Fellow. 

Research interests

Dr Lynch’s field of study is geometric analysis. He is particularly interested in using nonlinear elliptic and parabolic PDE to answer questions in geometry. He has made significant contributions to the analysis of singularities in geometric flows (mean curvature flow, fully nonlinear flows for hypersurfaces, Ricci flow). He also works on minimal submanifolds and their connection with semilinear PDE arising from the theory of phase-transitions (Allen--Cahn, Ginzburg--Landau). 

• Nonlinear PDE

• Riemannian geometry

• Geometric flows

• Minimal submanifolds

• Geometry of phase-transition models

Publications

Lynch, S. (2022). Convexity estimates for hypersurfaces moving by concave curvature functions. Duke Mathematical Journal, 171(10), 2047-2088.

Bourni, T., Langford, M., & Lynch, S. (2023). Collapsing and noncollapsing in convex ancient mean curvature flow. Journal für die reine und angewandte Mathematik (Crelles Journal), 2023(801), 273-305.

Guaraco, M. A., & Lynch, S. (2024). Plateau’s problem via the Allen–Cahn functional. Calculus of Variations and Partial Differential Equations, 63(5), 133.

Further information

Stephen Lynch's website