Dr Shengwen Wang

Profile

I am currently a lecturer in the school of mathematical sciences in Queen Mary University of London.

I do research in geometric analysis and partial differential equations. More specifically, I am interested in the regularity theory and singularity analysis of geometric partial differential equations (e.g. minimal surfaces, mean curvature flows, Ricci flows, Ginzburg-Landau and Allen-Cahn equations) and their applications in geometric topology and mathematical relativity.  

I obtained my PhD from Johns Hopkins University in 2018. Before joining QMUL as a lecturer, I have held postdoc positions in SUNY Binghamton, QMUL and Warwick.  

Curriculum vitae

Teaching

MTH 6151       Partial Differential Equations 

Research

Publications

• 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).

• Round spheres are Hausdorff stable under small perturbation of entropy. J. Reine Angew. Math. 758, 261-280 (2020).

• On the topological rigidity of self shrinkers in R^3. (Joint with Alexander Mramor). Int. Math. Res. Not. 2020, 1933-1941 (2020).

• The level set flow of a hypersurface in R^4 of low entropy does not disconnect. (Joint with Jacob Bernstein). Comm. Anal. Geom. 29, 1523-1543 (2021)

• Warped tori with almost non-negative scalar curvature. (Joint with Brian Allen, Lisandra Hernandez-Vazquez, Davide Parise, Alec Payne).  Geometriae Dedicata 200, 153-171 (2019).

• Integrability of scalar curvature and normal metric on conformally flat manifolds. (Joint with Yi Wang). J. Differential Equations 265, 1353-1370 (2018).

• Low entropy and the mean curvature flow with surgery. (Joint with Alexander Mramor). Calc. Var. Partial Differential Equations. 60, (2021) 

• 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). 

• Precise asymptotics near a generic S^1 × R^3 singularity of mean curvature flow. (Joint with Zhou Gang). To appear in Nonlinear Anal. 

• Second order estimates for transition layers and a curvature estimate for the parabolic Allen-Cahn. (Joint with Huy Nguyen). Int. Math. Res. Not. 2024, 6749-6789 (2024).

• Quantization of the energy for the inhomogeneous Allen-Cahn mean curvature. (Joint with Huy Nguyen). To appear in Math. Ann.