# Huy The Nguyen's Homepage

Dr Huy The Nguyen (Nguyễn Thế Huy)

School of Mathematical Sciences

Queen Mary University of London

Mile End Road

London E1 4NS

E-mail: h.nguyen@qmul.ac.uk

I am currently Reader in Geometry at Queen Mary University of London. Previously I was a lecturer at The University of Queensland and before that a postdoctoral fellow at the University of Warwick and the Max Planck Institute for Gravitational Physics (AEI). I completed my PhD at the Australian National University under the supervision of Professor Ben Andrews. My research interests are geometric analysis and differential geometry. My research focusses on geometric flows, particularly the Ricci flow, mean curvature flow and the Willmore flow, as well as conformal immersions of surfaces. I also have a strong interest in partial differential equations in particular the Allen-Cahn equation and the Ginzburg-Landau equation and their relationship to differential geometry and phase transitions.

I am currently the organiser of the QMUL Geometry and Analysis seminar. Details can be found at the departmental webpage. I also co-organise the QMUL geometric analysis seminar. In this seminar, we discuss research level topics appropriate for beginning PhD students in geometric analysis. If you wish to be added to the mailing list for this seminar, please email me at h.nguyen@qmul.ac.uk.

Recently I was awarded a grant from the EPSRC "Geometric Flows and the Dynamics of Phase Transitions". This grant will run for three years from 1 December 2023 to 30 November 2026. Further information can be found here.

Previously I was awarded (together with Reto Buzano) a grant from the EPSRC “Advances in Mean Curvature Flow: Theory and Applications". This grant ran from 1 January 2019 until 30 September 2022. Further information can be found here.

## Preprints

Singularity Models for High Codimension Mean Curvature Flow in Riemannian Manifolds (joint with Artemis A. Vogiatzi)

Noncompact self-shrinkers for mean curvature flow with arbitrary genus (joint with Reto Buzano and Mario B. Schulz)

Quadratically pinched submanifolds of the sphere via mean curvature flow with surgery (joint with Mat Langford and Stephen Lynch)

Brakke Regularity for the Allen-Cahn Flow (joint with Shengwen Wang)

Sharp pinching estimates for mean curvature flow in the sphere (joint with Mat Langford)

Cylindrical Estimates for High Codimension Mean Curvature Flow

## Papers

Quantization of the Energy for the inhomogeneous Allen-Cahn mean curvature (joint with Shengwen Wang, Mathematische Annalen (2024))

Second order estimates for transition layers and a curvature estimate for the parabolic Allen-Cahn ( joint with Shengwen Wang, IMRN, 2024:8 (2024), pp 6759–6789)

Evolving Pinched Submanifolds of the Sphere by Mean Curvature Flow (joint with Charles Baker) Mathematische Zeitschrift 303, 50 (2023)

Convexity Estimates for High Codimension Mean Curvature Flow (joint with Stephen Lynch, Mathematische Annalen 388, pp 575–613, (2024))

Quadratically pinched hypersurfaces of the sphere via mean curvature flow with surgery (joint with Mat Langford) Calc. Var. PDE 60:216 (2021)

Pinched Ancient Solutions to the High Codimension Mean Curvature Flow (joint with Stephen Lynch) Calc. of Var. PDE 60:29 (2021)

The higher-dimensional Chern-Gauss-Bonnet formula for singular conformally flat manifolds (joint with Reto Buzano), J. Geom. Anal. 29:2 (2019), pp 1043–1074

Surfaces of co-dimension two pinched by normal curvature (joint with Charles Baker), Annales de l'Institut Henri Poincare (C) Non Linear Analysis 34:6 (2017), pp 1599-1610

The Chern-Gauss-Bonnet formula for singular non-compact four-dimensional manifolds (joint with Reto Buzano) Comm. Anal. Geom. 27:8 (2019), pp 1697–1736

Global conformal invariants of submanifolds (joint with Andrea Mondino, Annales de l'Institut Fourier, 68 (2018), pp. 2663-2695)

Branched Willmore spheres (joint with Tobias Lamm, Journal für die reine und angewandte Mathematik (Crelle’s Journal), 701 (2015), pp 169-194)

Convexity and cylindrical estimates for mean curvature flow in the sphere (Transactions of the AMS, 367, (2015), pp 4517-4536)

A gap theorem for Willmore tori and an application to the Willmore Flow (joint with Andrea Mondino), Nonlinear Analysis:Theory, Methods and Analysis, 02 (2014), pp 220–225)

Quantitative rigidity results for conformal immersions (joint with Tobias Lamm), American Journal of Mathematics, 136, 2014, Issue 5, pp 1409-1440)

Geometric rigidity for sequences of $ W^{2,2}$ conformal immersions Calc. Var. PDE, 49 (2014), Issue 3-4, pp 1337-1357 (available from Springerlink)

Geometric rigidity for analytic estimates of Müller-Šverák, Mathematische Zeitschrift, 272 (2012), no. 3-4, pp 1059-1074

Four-manifolds with $1/4$-pinched flag curvatures, (joint with Ben Andrews), Asian Journal of Mathematics, 13, (2009), no. 2, pp 251-270

Isotropic Curvature and the Ricci flow, International Mathematical Research Notices, (2010), no. 3, pp 536-558

Links

The following is a link to a page maintained by John Lott relating to the Ricci flow, Geometrization of Three Manifolds and Poincaré's Conjecture. Notes and commentary on Perelman's Ricci flow papers.

The Clay Institute also maintains a page on material related to the Poincaré Conjecture.

A very good overview of current research in geometric flows is given by Surveys in Differential Geometry Vol XII: Geometric flows.