Preprints

1. Singularity formation and self-shrinkers for the parabolic Bernoulli problem (with Hunter Liu and Zihui Zhao)

56 pages. Under review at Anal. PDE, 2026.

2. Space-time geometry of Hele-Shaw flow (with Carson Collins and Inwon Kim)

50 pages. Under review at Arch. Ration. Mech. Anal., 2026.

3. The optimal rate of convergence in mean field control via recoupled shadow flows

48 pages. Under review at Ann. Probab., 2026.

4. Uniqueness of synchronized stationary equilibria in the Kuramoto mean field game 

16 pages. Under review at Math. Oper. Res., 2026.

5. Optimal regularity at the free boundary in one-dimensional first-order mean field games

18 pages. Under review at Calc. Var. Partial Differ. Equ., 2026.

6. Master equations with an individual noise on finite state graphs (with Wilfrid Gangbo, Jeremy Wu, and Zhaoyu Zhang).

30 pages. Under review at SIAM J. Control Optim., 2026.

7. The supercooled Stefan problem: fractal freezing and the fine structure of maximal solutions (with Raymond Chu and Inwon Kim).

42 pages. Under review at Comm. Pure Appl. Math., 2025.

8. Regularity of the free boundary for the supercooled Stefan problem in arbitrary dimensions (with Max Engelstein and Inwon Kim).

44 pages. Under review at Duke Math J., 2025.

9. Free boundary regularity and well-posedness of physical solutions to the supercooled Stefan problem 

25 pages. Revision submitted, Probab. Theory Related Fields, 2025.

10. Self-similar intermediate asymptotics for first-order mean field games

40 pages. Under review at  J. Math. Pures Appl., 2025.