My research is partially supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. RS-2023-00252516), the 2023 Research Fund of the University of Seoul, and the POSCO Science Fellowship of POSCO TJ Park Foundation.
Mean curvature flows & gradient flows
Area-Preserving Anisotropic Mean Curvature Flow in Two Dimensions (with Eric Kim)
Level-Set Forced Mean Curvature Flow With the Neumann Boundary Condition (with Jiwoong Jang, Hiroyoshi Mitake, and Hung Vinh Tran), Journal de Mathématiques Pures et Appliquées, 168:143-167, 2022 [arxiv] [Video]
On Volume-Preserving Crystalline Mean Curvature Flow (with Inwon Kim and Norbert Požár). Mathematische Annalen, 384(1), 1-42, 2022 [arxiv] [Slides]
Degenerate Nonlinear Parabolic Equations With Discontinuous Diffusion Coefficients (with Alpár Richárd Mészáros), Journal of the London Mathematical Society, 104(2), 688-746, 2021 [arxiv] [Slides]
Volume Preserving Mean Curvature Flow for Star-Shaped Sets (with Inwon Kim). Calculus of Variations and Partial Differential Equations, 59(2), 2020 [arxiv] [Slides]
On Mean Curvature Flow with Forcing (with Inwon Kim). Communications in Partial Differential Equations. 45(5):414-455, 2020 [arXiv]
Dispersal Toward Food: A Study of a Singular Limit of an Allen-Cahn Equation (with Danielle Hilhorst, Yong Jung Kim, and Thanh Nam Nguyen). Journal of Mathematical Biology, 76(3):531-565, 2018
Optimal transport, optimization & applications to machine learning
On the Complexity of First-Order Methods in Stochastic Bilevel Optimization (with Jeongyeol Kwon and Hanbaek Lyu)
Memorization Capacity for Additive Fine-Tuning (with Jy-yong Sohn, Seoyeon An, Kangwook Lee), to appear in The 40th Conference on Uncertainty in Artificial Intelligence (UAI 2024)
On Penalty Methods for Nonconvex Bilevel Optimization and First-Order Stochastic Approximation (with Jeongyeol Kwon, Stephen Wright, and Robert Nowak), to appear in The Twelfth International Conference on Learning Representations, (ICLR 2024, Spotlight) [arXiv]
Complexity of Block Coordinate Descent With Proximal Regularization and Applications to Wasserstein Cp-Dictionary Learning (with Hanbaek Lyu), The 40th International Conference on Machine Learning (ICML 2023) [arXiv]
A Fully First-Order Method for Stochastic Bilevel Optimization (with Jeongyeol Kwon, Stephen Wright, and Robert Nowak), The 40th International Conference on Machine Learning (ICML 2023, Oral) [arXiv]
Score-Based Generative Modeling Secretly Minimizes the Wasserstein Distance (with Kangwook Lee and Ying Fan), Advances in Neural Information Processing Systems 35 (NeurIPS 2022) [arxiv] [Short Video] [Long Video (Korean)]
Training Wasserstein GANs Without Gradient Penalties (with Guido Montúfar, Yeoneung Kim, and Insoon Yang) [Slides] [Video1] [Video2]
Hamilton-Jacobi equation, optimal control & applications to multi-agent system
The Regularity with Respect to Domains of the Additive Eigenvalues of Superquadratic Hamilton-Jacobi Equation and Related Vanishing Discount Problems (with Farid Bozorgnia and Son N.T. Tu)
Cucker-Smale Type Flocking Models on a Sphere (with Sun-Ho Choi and Hyowon Seo), Journal of Mathematical Physics, 65 (4): 042701, 2024 [arXiv]
Target Tracking Systems on a Sphere With Topographic Information (with Sun-Ho Choi, Hyowon Seo, and Soyeong Jeong), IEEE Transactions on Cybernetics, 2023
Multi-Agent System for Target Tracking on a Sphere and Its Asymptotic Behavior (with Sun-Ho Choi and Hyowon Seo), Communications in Nonlinear Science and Numerical Simulation, 117, 106967, 2023 [arxiv]
Flocking Formation and Stabilizer of Boosted Cooperative Control on a Sphere (with Sun-Ho Choi and Hyowon Seo)
Uniform Position Alignment Estimate of Spherical Flocking Model With Inter-Particle Bonding Forces (with Sun-Ho Choi and Hyowon Seo)
Thesis
Mean Curvature Flows with Forcing and Degenerate Nonlinear Parabolic Equations. Dissertation, UCLA, 2020
Collaborators
Seoyeon An (Seoul, South Korea)
Farid Bozorgnia (Lisboa, Portugal)
Sun-Ho Choi (Yongin, South Korea)
Ying Fan (Madison, USA)
Danielle Hilhorst (Paris, France)
Jiwoong Jang (Madison, USA)
Inwon Kim (Los Angeles, USA)
Eric Kim (Los Angeles, USA)
Yeoneung Kim (Seoul, South Korea)
Yong Jung Kim (Daejeon, South Korea)
Jeongyeol Kwon (Madison, USA)
Kangwook Lee (Madison, USA)
Hanbaek Lyu (Madison, USA)
Alpár Richárd Mészáros (Durham, UK)
Guido Montúfar (Los Angeles, USA / Leipzig, Germany)
Hiroyoshi Mitake (Tokyo, Japan)
Thanh Nam Nguyen (Paris, France)
Robert Nowak (Madison, USA)
Norbert Požár (Kanazawa, Japan)
Jy-yong Sohn (Seoul, South Korea)
Hyowon Seo (Yongin, South Korea)
Hung Vinh Tran (Madison, USA)
Son N.T. Tu (Michigan, USA)
Stephen Wright (Madison, USA)
Insoon Yang (Seoul, South Korea)