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Stephen Lynch

Dr Stephen Lynch

Lecturer in Pure Mathematics

Research interests

  • Mathematics

Biography

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

Further information

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.

Stephen Lynch's website

Research

ARTICLE Graphs Blue
Analysis

The Analysis Group's research interests focus mainly on PDEs, operator theory and spectral theory.

Geometry research group 780 x 440
Geometry

The Geometry Group focuses on topics within the following areas: algebraic geometry, cohomology theories, differential geometry, geometric analysis, homogeneous space, Lie groups, mirror symmetry, and symplectic geometry.

Research

ARTICLE Graphs Blue
Analysis

The Analysis Group's research interests focus mainly on PDEs, operator theory and spectral theory.

Geometry research group 780 x 440
Geometry

The Geometry Group focuses on topics within the following areas: algebraic geometry, cohomology theories, differential geometry, geometric analysis, homogeneous space, Lie groups, mirror symmetry, and symplectic geometry.