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 

1.  (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]

2.  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]

3. (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]

4. (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]

5. (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]

6. Ancient solutions to the Curve Shortening Flow spanning the halfplane, Trans. Am. Math. Soc. 374, No. 6, 4207-4226 (2021). [arXiv version], [journal link]

7. (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]

8. (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] 

9.  (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].

10. (Joint with Chen, J.) Compactness of Hamiltonian stationary Lagrangian submanifold in symplectic manifolds, to appear in Trans. Amer. Math. Soc.  [arXiv version].

Preprint/In preparation: 

11. 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. 

Seminar/talks

• (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]