Sung-Jin Oh

Miller Research Fellow

Department of Mathematics
University of California, Berkeley
Berkeley, CA


Office: 887 Evans Hall

E-mail:

I have moved to Korea Institute for Advanced Study.
This homepage is no longer maintained.

I am a Miller Research Fellow in the Department of Mathematics at UC Berkeley. My host is Professor Daniel Tataru. I did my Ph.D. in mathematics at Princeton University. My adviser was Professor Sergiu Klainerman. For my undergraduate work, I went to KAIST.

Curriculum Vitae pdf
Research Interests

I am interested in geometric PDEs, especially those which originate from physics. I enjoy thinking about these PDEs since their understanding requires combining ideas from a diverse range of fields, such as harmonic analysis, differential geometry and physics. Specific equations that I have considered so far include the Yang-Mills equations, Einstein equations, various Chern-Simons theories, wave maps and incompressible Euler equations.

Papers & Preprints
1 Solutions to the Einstein-scalar-field system in spherical symmetry with large bounded variation norms, with J. Luk and S. Yang. arXiv:1605.03893 [gr-qc].
2 Global well-posedness of high dimensional Maxwell-Dirac for small critical data, with C. Gavrus. arXiv:1604.07900 [math.AP]
3 Small data global existence and decay for relativistic Chern-Simons equations, with M. Chae. arXiv:1512.03039 [math.AP]
4 The Cauchy problem for wave maps on hyperbolic space in dimensions d≥4, with A. Lawrie and S. Shahshahani. arXiv:1510.04296 [math.AP]
5 On Nonperiodic Euler Flows with Hölder Regularity, with P. Isett, to appear in Arch. Rational Mech. Anal. (ARMA). preprint.
(This manuscript is the first part of the arXiv preprint arXiv:1402.2305, split and submitted separately per requested by the journal.)
6 On the Kinetic Energy profile of Hölder continuous Euler flows, with P. Isett, to appear in Annales d'IHP (C). preprint.
(This manuscript is the second part of the preprint arXiv:1402.2305.)
7 Equivariant Wave Maps on the Hyperbolic Plane with Large Energy, with A. Lawrie and S. Shahshahani, to appear in Math. Res. Lett. arXiv:1505.03728 [math.AP]
8 Local well-posedness of the (4+1)-dimensional Maxwell-Klein-Gordon equation, with D. Tataru, to appear in Annals of PDE. arXiv:1503.01560 [math.AP]
9 Energy dispersed large energy solutions to the (4+1) dimensional Maxwell-Klein-Gordon equation, with D. Tataru, to appear in Amer. J. Math. arXiv:1503.01561 [math.AP]
10 Finite energy global well-posedness and scattering of the (4+1) dimensional Maxwell-Klein-Gordon equation, with D. Tataru, to appear in Invent. Math. arXiv:1503.01562 [math.AP]
11 A refined threshold theorem for (1+2)-dimensional wave maps into surfaces, with A. Lawrie, to appear in Comm. Math. Phys. arXiv:1502.03435 [math.AP]
12 Gap Eigenvalues and Asymptotic Dynamics of Geometric Wave Equations on Hyperbolic Space, with A. Lawrie and S. Shahshahani. arXiv:1502.00697 [math.AP]
13 Proof of linear instability of the Reissner-Nordström Cauchy horizon under scalar perturbations, with J. Luk, to appear in Duke Math. J. arXiv:1501.04598 [gr-qc]
14 Profile decomposition for wave equations on hyperbolic space with applications, with A. Lawrie and S. Shahshahani, to appear in Math. Ann. arXiv:1410.5847 [math.AP]
15 Stability of stationary equivariant wave maps from the hyperbolic plane, with A. Lawrie and S. Shahshahani. arXiv:1402.5981 [math.AP]
16 Quantitative decay rates for dispersive solutions to the Einstein-scalar field system in spherical symmetry, with J. Luk, Analysis & PDE. Vol. 8, No. 7 (2015), pp. 1603–1674. arXiv:1402.2984 [gr-qc]
17 Decay and scattering for the Chern-Simons-Schrödinger equations, with F. Pusateri, to appear in Int. Math. Res. Not. (IMRN). arXiv:1311.2088 [math.AP]
18 A heat flow approach to Onsager's conjecture for the Euler equations on manifolds, with P. Isett, to appear in Trans. Amer. Math. Soc. arXiv:1310.7947 [math.AP]
19 Finite energy global well-posedness of the Chern-Simons-Higgs equations in the Coulomb gauge. arXiv:1310.3955 [math.AP]
20 Gauge choice for the Yang-Mills equations using the Yang-Mills heat flow and local well-posedness in H^{1}, J. Hyper. Diff. Equ. Vol. 11, No. 01, pp. 1- 108. arXiv:1210.1558 [math.AP].
21 Finite Energy Global Well-posedness of the Yang-Mills equations on $\mathbb{R}^{1+3}$: An Approach Using the Yang-Mills Heat Flow, Duke Math. J. Vol. 164, No. 9 (2015), pp. 1669-1732 arXiv:1210.1557 [math.AP].
22 Low regularity solutions to the Chern-Simons-Dirac and the Chern-Simons-Higgs equations in the Lorenz gauge, with H. Huh, to appear in Comm. Partial Differential Equations. arXiv:1209.3841[math.AP]
Ph.D. Thesis
Finite energy global well-posedness of the (3+1)-dimensional Yang-Mills equations using a novel Yang-Mills heat flow gauge. pdf
Teaching

In Spring 2015, I gave a mini-course under MAT290 (Nonlinear Hyperbolic PDEs).

Online talks
- Linear instability of the Cauchy horizon in subextremal Reissner-Nordström spacetime under scalar perturbations. Mathematical Problems in General Relativity, Stony Brook, NY, USA. Jan 20, 2014. video
- Stability of stationary equivariant wave maps from the hyperbolic plane. Dynamics in Geometric Dispersive Equations and the Effects of Trapping, Scattering and Weak Turbulence, Banff, Alberta, Canada. May 5, 2014. video
Notes
1 Lecture notes on linear wave equation. (Based on guest lectures in MAT222 at UC Berkeley, Fall 2014) pdf
2 Counterexample for sharp trace theorem. pdf