# 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). arXiv:2305.00363

Ancient solutions of Ricci flow with Type I curvature growth (w. Andoni Royo Abrego). To appear in J. Geom. Anal. 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). To appear in Math. Annalen. 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 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