Sunghan Kim

Overview

I am an assistant professor at KTH, since August 2026. My research centers on the mathematical analysis of PDEs, specializing in free boundary problems, homogenization problems, and degenerate/singular PDEs. Before returning to KTH, I was on the faculty and completed a postdoctoral fellowship at Uppsala University (working with Kaj Nyström), and previously held a postdoctoral position at KTH hosted by Henrik Shahgholian. I earned my Ph.D. in 2019 from Seoul National University under Ki-Ahm Lee. My current work is supported by a VR Starting Grant and the Göran Gustafsson Prize for Young Researchers.

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Research Focus

Much of my recent work focuses on the study of Constraint Maps, a natural extension of the classical obstacle problem to a vectorial setting. Due to topological constraints, these maps exhibit rich phenomena combining harmonic map singularities, branch points akin to minimal surfaces, and free boundaries. A central theme in my recent work investigates the fundamental interaction between these structures:does the free boundary meet the mapping singularities?

• Constraint maps and free boundaries (with A. Figalli, A. Guerra, and H. Shahgholian), Notices of the AMS, 72 (2025), 494–503.

• Constraint maps with free boundaries: the Bernoulli case (with A. Figalli, A. Guerra, and H. Shahgholian), J. Eur. Math. Soc., published online first, 2025.

• Constraint maps with free boundaries: the obstacle case (with A. Figalli and H. Shahgholian), Arch. Ration. Mech. Anal., 248 (2024), no. 79.

• Constraint maps: singularities vs free boundaries (with A. Figalli, A. Guerra, and H. Shahgholian), preprint, 2024.