I am broadly interested in Differential Geometry and Partial Differential Equations. More specifically, I work in problems related to geometric flows and geometry of Lagrangian submanifolds.
I am broadly interested in Differential Geometry and Partial Differential Equations. More specifically, I work in problems related to geometric flows and geometry of Lagrangian submanifolds.
Research Articles:
In press/Accepted
(Joint with Chen, J.) The space of compact self-shrinking solutions to the Lagrangian mean curvature flow in C^2, J. Reine Angew. Math. 743, 229-244 (2018). [arXiv version], [journal link]
Parabolic Omori-Yau maximum principle for mean curvature flow and some applications, J. Geom. Anal. 28, No. 4, 3183-3195 (2018). [arXiv version], [journal link]
(Joint with Lee, M.-C.) Uniqueness Theorem for non-compact mean curvature flow with possibly unbounded curvatures, Comm. Anal. Geom. 29 (2021), no. 6, 1475–1508. [arXiv version], [journal link]
(Joint with Chen, J.) Geometry of Lagrangian self-shrinking tori and applications to the Piecewise Lagrangian Mean Curvature Flow, Am. J. Math. 143, No. 1, 227-264 (2021). [arXiv version], [journal link]
(Joint with Chen, J.) On the Compactness of Hamiltonian Stationary Lagrangian Surfaces in Kähler Surfaces, Calc. Var. Partial Differ. Equ. 60, No. 2, Paper No. 75, 23 p. (2021). [arXiv version], [journal link]
Ancient solutions to the Curve Shortening Flow spanning the halfplane, Trans. Am. Math. Soc. 374, No. 6, 4207-4226 (2021). [arXiv version], [journal link]
(Joint with Muhammad, A. and Møller, N. M.) Entropy Bounds, Compactness and Finiteness Theorems for Embedded Self-shrinkers with Rotational Symmetry, J. Reine Angew. Math. 793, 239-259 (2022) [arXiv version], [journal link]
(Joint with Ooi, S.Y. and Pyo, J.) Rigidity results for graphical translators for the mean curvature flow moving in non-graphical direction, Proc. Amer. Math. Soc. 151 (2023), 5391-5402. [arXiv version], [journal link]
(Joint with Muhammad, A.) Entropy bounds for self-shrinkers with symmetries, J Geom. Anal. 34, 36 (2024). https://doi.org/10.1007/s12220-023-01482-9 [arXiv version], [journal link].
(Joint with Chen, J.) Compactness of Hamiltonian stationary Lagrangian submanifold in symplectic manifolds, Trans. Amer. Math. Soc. 377 (2024), 6151-6170 [arXiv version], [journal link].
(Joint with Dasong Li) Backward Uniquessness of extrinsic geometric flow in general ambient manifold, Calc. Var. Partial Differ. Equ. 64, 236 (2025) [arXiv version ], [journal link] , SharedIT
Preprint/In preparation:
Blowdown and entropy of embedded translators in R^3, in preparation.
Conference/Workshop organized
First Young Geometers Meetings - on Geometric Analysis and Differential Geometry, University of Copenhagen, April 2021.
Mean Curvature Flow and Related Topics, University of Copenhagen, March 2022.
SUSTech mini-workshop in Geometric Analysis, August 2024.
SUSTech mini-workshop in Geometric Analysis: Recent Advances in Ricci Flow and related topics, August 2025.
Seminar/talks
(May 2025) Workshop on Celebrating 100 years of the Math building at UBC [link]
(Jul. 2024) Workshop on Minimal Surfaces and Mean Curvature Flow 2024, BICMR, Peking U. [link]
(Jul. 2024) The 4th Symposium in Geometry and Differential Equations, IGP, USTC [link]
(Aug. 2023) BIRS workshop "Non-linear critical point theory in analysis and geometry", Kelowna, BC [link]
(Jul. 2023) 29th Nordic Congress in Mathematics, Aalborg (Geometry session) [link]
(Dec. 2022) Joint UHH-UCPH Workshop on Geometric Analysis, University of Hamburg
(Nov. 2022) Geometric Analysis Seminar, The Chinese University of Hong Kong [link]
(Sep. 2022) DG/PDE Seminar, University of Washington, Seattle [link]
(Aug. 2022) Seminar, BRL Busan National University
(Jul. 2022) CGP seminar, IBS Center of Geometry and Physics [link]
(Jun. 2022) Geometry seminar, Korea Institute of Advanced Studies
(May 2022) GAPPF seminars, Jeonbuk National University [link]
(Apr. 2022) Differential geometry seminar, University of British Columbia [link]
(Dec. 2020) An Invitation to Geometric Analysis, seminar, Jeonbuk National University
(May 2020) Non-linear Analysis seminar, Rutgers, the State University of New Jersey, (Cancelled)
(Oct. 2019) AMS Eastern sectional meeting, Binghamton University, the State University of New York [link]
(Aug. 2019) Pure Mathematics Seminar, University of Science and Technology, Hong Kong
(Jul. 2019) Geometric Analysis Seminar, the Chinese University of Hong Kong [link]
(May 2019) PIMS CRG Workshop on Geometric Analysis, University of British Columbia [link]
(May 2019) Analysis Seminar, Binghamton University, the State University of New York
(Jul. 2018) Geometric Analysis Seminar, the Chinese University of Hong Kong [link]
(May 2018) Annual Meeting, Hong Kong Mathematics Society
(Oct. 2017) Geometry and Analysis Seminar, Columbia University
(Sep. 2017) Geometric Analysis Seminar, Rutgers, the State University of New Jersey
(Feb. 2017) Geometric Analysis Seminar, Univeristy of Oregon
(Jan. 2017) Geometric Analysis Seminar, University of Chicago
(Dec. 2016) 2016 NCTS Workshop on Geometric Analysis [link]
(Nov. 2016) Differential Geometry Seminar, University of California, Irvine
(Dec. 2015) 2015 SIAM Conference on Analysis of Partial Differential Equations [link]