Welcome to Shengwen's website!

Teaching:

Math 371         Ordinary differential equations                   2018 Fall, Binghamton University

Math 590F       Topics in Analysis                                                 2019 Spring, Binghamton University

Math 371         Ordinary differential equations                   2019 Spring, Binghamton University

LTCC course   Introduction to mean curvature flow       2020 Fall, London (online)

MA4C0             Differential Geometry                                       2021  Fall, University of Warwick

MTH 6151       Partial Differential Equations                       2022 Fall, Queen Mary University of London

MTH 6151       Partial Differential Equations                       2023 Fall, Queen Mary University of London

MTH 6151       Partial Differential Equations                       2024 Fall, Queen Mary University of London

MTH 5113       Introduction to Differential Geometry    2025 Spring, Queen Mary University of London

MTH 6151       Partial Differential Equations                       2025 Fall, Queen Mary University of London

LTCC course   Elliptic Partial Differential Equations       2026 Spring, London Mathematical Society

SEF041             Mathematics B                                                        2026 Spring, Queen Mary University of London

Office hour: 

Research interest:

Geometric analysis and geometric PDEs. I am interested in understanding the formation of singularities and developing/improving regularity theory of geometric partial differential equations such as minimal surfaces, mean curvature flows, Allen-Cahn and Ginzburg-Landau equations, etc.

Publications and preprints:

• Some properties of closed hypersurfaces of small entropy and the topology of hypersurfaces through singularities of mean curvature flow.  

         ETD - Doctoral Dissertations. Johns Hopkins University (2018). [Link]

• Round spheres are Hausdorff stable under small perturbation of entropy.  

         J. Reine Angew. Math. 758, 261-280 (2020). [Link]

• On the topological rigidity of self shrinkers in R^3. (with Alexander Mramor) 

         Int. Math. Res. Not. 2020, 1933-1941 (2020). [Link]

• The level set flow of a hypersurface in R^4 of low entropy does not disconnect. (with Jacob Bernstein)

         Comm. Anal. Geom. 29, 1523-1543 (2021). [Link]

• Warped tori with almost non-negative scalar curvature. (with Brian Allen, Lisandra Hernandez-Vazquez, Davide Parise, Alec Payne)

         Geometriae Dedicata 200, 153-171 (2019). [Link]

• Integrability of scalar curvature and normal metric on conformally flat manifolds. (with Yi Wang)

         J. Differential Equations 265, 1353-1370 (2018). [Link]

• Low entropy and the mean curvature flow with surgery. (with Alexander Mramor) 

         Calc. Var. Partial Differential Equations. 60, (2021) [Link]

• Extended abstract "The level set flow of a hypersurface in R^4 of low entropy does not disconnect" in the Proceedings of the John H. Barrett Memorial Lectures at the University of Tennessee, Knoxville, May 29 - June 1, 2018 (edited by Theodora Bourni and Mat Langford). 

         De Gruyter Proc. Math. (2020).  [Link]

• Precise asymptotics near a generic S1 × R3 singularity of mean curvature flow.  (with Gang Zhou) 

         To appear in Nonlinear Anal. [Link]

• Second order estimates for transition layers and a curvature estimate for the parabolic Allen-Cahn.  (with Huy Nguyen) 

         Int. Math. Res. Not. 2024, 6759-6789 (2024) [Link]

• Brakke regularity for the Allen-Cahn flow.  (with Huy Nguyen) 

         Preprint. [Link]

• Quantization of the energy for the inhomogeneous Allen-Cahn mean curvature.  (with Huy Nguyen) 

         To appear in Math. Ann. [Link]

• Allard regularity for Abelian Yang-Mills-Higgs equation.  (with Huy Nguyen) 

         Preprint. [Link]