Stephen Lynch
stephen dot lynch at imperial.ac.uk
Department of Mathematics
Imperial College London
South Kensington
SW7 2AZ London
I'm a Chapman Fellow at Imperial College London. My research is in geometric analysis, with emphasis on geometric flows such as the mean curvature flow. These are nonlinear parabolic evolution equations that deform submanifolds in a Euclidean or Riemannian background space, and typically exhibit singularity formation. One fundamental goal is to determine the structure of singularities and find ways to flow past them. In situations where this has been achieved, interesting results in geometry and topology have followed.
I obtained a PhD in Tübingen under the supervision of Gerhard Huisken. Prior to that I did a Master's at the Berlin Mathematical School with Klaus Ecker and Mat Langford. I was an undergraduate at the University of Queensland, where I did honours with Joe Grotowski and Artem Pulemotov.
Papers
Rotational symmetry of ancient solutions to fully nonlinear curvature flows (w. A. Cogo and O. Vičánek Martínez). arXiv:2310.08301.
A differential Harnack inequality for noncompact evolving hypersurfaces. arXiv:2310.07369.
Plateau's problem via the Allen--Cahn functional (w. Marco A. M. Guaraco). To appear in Calc. Var. and PDE. arXiv:2305.00363.
Ancient solutions of Ricci flow with Type I curvature growth (w. Andoni Royo Abrego). J. Geom. Anal 34 (2022). arXiv:2211.06253.
Collapsing and noncollapsing in convex ancient mean curvature flow (w. Theodora Bourni & Mat Langford). J. für Reine Angew. Math. 801 (2023). arXiv:2106.06339.
Uniqueness of convex ancient solutions to hypersurface flows, J. für Reine Angew. Math. 788 (2022). arXiv:2103.02314.
Convexity estimates for hypersurfaces moving by concave curvature functions, Duke Math. J. 171 (2022). arXiv:2007.07791.
Convexity estimates for high codimension mean curvature flow (w. Huy The Nguyen). Math. Annalen 388 (2024). arXiv:2006.05227.
Pinched ancient solutions to the high codimension mean curvature flow (w. Huy The Nguyen), Calc. Var. and PDE 60 (2020). arXiv:1709.09697.
Sharp one-sided curvature estimates for fully nonlinear curvature flows with applications to ancient solutions (w. Mat Langford), J. für Reine Angew. Math. 765 (2020). arXiv:1704.03802.
My thesis can be found here.
Talks
Geometry Analysis Seminar, University of Copenhagen, 2024
London PDE Seminar, QMUL, 2024
Geometry Seminar, UCL, 2024
Analysis Seminar, KCL, 2023
PDE Seminar, Oxford, 2023
Nonlinear Critical Point Theory in Analysis and Geometry, BIRS Kelowna, 2023
Geometric Analysis Seminar, University of Chicago, 2023
Geometric Analysis Seminar, Knoxville, 2023
Geometry and Topology Seminar, Caltech, 2023
Geometric analysis and mathematical relativity, Hebrew University Jerusalem, 2023
Geometric Partial Differential Equations, Warwick, 2022
Geometric Analysis Seminar, MIT, 2022
Geometry & Analysis Seminar, Columbia, 2022
Oberseminar Differentialgeometrie, Münster, 2022
London Geometry and Topology Seminar, Imperial College, 2022
Analysis Seminar, Leeds, 2022
Mean curvature flow and related topics, Queen Mary London, 2022
FHST Meeting Geometry and Analysis, Stuttgart, 2022
Geometric Analysis, Differential Geometry and Relativity, Potsdam/Tuebingen, 2022
Analysis Seminar, Johns Hopkins, 2022
Pure Maths Seminar, University of Queensland, 2022
The University of Newcastle, 2022
PDE and Analysis Seminar, ANU, 2022
MATRIX-SMRI Symposium 'Singularities in Geometric Flows', 2022