
SungJin OhCMC Research Professor Korea Institute for Advanced Study (KIAS) Office: 8318 Email: 
I am a CMC Research Professor in Korea Institute for Advanced Study (KIAS). Previously, I was a Miller Research Fellow in the Department of Mathematics at UC Berkeley. My host was Daniel Tataru. I did my Ph.D. in mathematics at Princeton University. My adviser was 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 YangMills equations, Einstein equations, various ChernSimons theories, wave maps and incompressible Euler equations. 
Papers & Preprints  
30  Local smoothing estimates for Schrödinger equations on hyperbolic space, with A. Lawrie, J. Luehrmann and S. Shahshahani. arXiv:1808.04777 [math.AP] 
(The following four papers constitute a series, whose overview is provided in the summary below.)  
29  The YangMills heat flow and the caloric gauge, with D. Tataru. arXiv:1709.08599 [math.AP]. 
28  The hyperbolic YangMills equation in the caloric gauge. Local wellposedness and control of energy dispersed solutions, with D. Tataru. arXiv:1709.09332 [math.AP]. 
27  The hyperbolic YangMills equation for connections in an arbitrary topological class, with D. Tataru, to appear in Comm. Math. Phys. arXiv:1709.08604 [math.AP]. 
26  The threshold conjecture for the energy critical hyperbolic YangMills equation, with D. Tataru. arXiv:1709.08606 [math.AP]. 
(The following two papers constitute a series; for an overview, see Section 1.1 of Paper 25.)  
25  Strong cosmic censorship in spherical symmetry for twoended asymptotically flat initial data I. The interior of the black hole region, with J. Luk. arXiv:1702.05715 [grqc]. 
24  Strong cosmic censorship in spherical symmetry for twoended asymptotically flat initial data II. The exterior of the black hole region, with J. Luk. arXiv:1702.05716 [grqc]. 
23  Dynamical black holes with prescribed masses in spherical symmetry, with J. Luk and S. Yang. arXiv:1702.05717 [grqc]. 
22  Solutions to the Einsteinscalarfield system in spherical symmetry with large bounded variation norms, with J. Luk and S. Yang, to appear in Ann. PDE. arXiv:1605.03893 [grqc]. 
21  Global wellposedness of high dimensional MaxwellDirac for small critical data, with C. Gavrus, to appear in Mem. Amer. Math. Soc. arXiv:1604.07900 [math.AP] 
20  Small data global existence and decay for relativistic ChernSimons equations, with M. Chae, to appear in Annales Henri Poincaré. arXiv:1512.03039 [math.AP] 
19  The Cauchy problem for wave maps on hyperbolic space in dimensions d≥4, with A. Lawrie and S. Shahshahani, to appear in Int. Math. Res. Not. (IMRN) arXiv:1510.04296 [math.AP] 
(The following two papers are parts of the preprint arXiv:1402.2305, split per journal's request.)  
18  On Nonperiodic Euler Flows with Hölder Regularity, with P. Isett, Arch. Rational Mech. Anal. (ARMA) Vol. 221 (2016), No. 2, pp. 725804. preprint. 
17  On the Kinetic Energy profile of Hölder continuous Euler flows, with P. Isett, to appear in Annales d'IHP (C). preprint. 
16  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] 
(The following three papers constitute a series; for an overview, see Sections 23 of Paper 13.)  
15  Local wellposedness of the (4+1)dimensional MaxwellKleinGordon equation, with D. Tataru, Annals of PDE. Vol. 2 (2016), No. 1. arXiv:1503.01560 [math.AP] 
14  Energy dispersed large energy solutions to the (4+1) dimensional MaxwellKleinGordon equation, with D. Tataru, to appear in Amer. J. Math. arXiv:1503.01561 [math.AP] 
13  Finite energy global wellposedness and scattering of the (4+1) dimensional MaxwellKleinGordon equation, with D. Tataru, Invent. Math. Vol. 205, (2016), no. 3, pp. 781–877. arXiv:1503.01562 [math.AP] 
12  A refined threshold theorem for (1+2)dimensional wave maps into surfaces, with A. Lawrie, Comm. Math. Phys. Vol. 342, (2016), no. 3, pp. 989999. arXiv:1502.03435 [math.AP] 
11  Gap Eigenvalues and Asymptotic Dynamics of Geometric Wave Equations on Hyperbolic Space, with A. Lawrie and S. Shahshahani, to appear in J. Funct. Anal. arXiv:1502.00697 [math.AP] 
10  Proof of linear instability of the ReissnerNordström Cauchy horizon under scalar perturbations, with J. Luk, to appear in Duke Math. J. arXiv:1501.04598 [grqc] 
9  Profile decomposition for wave equations on hyperbolic space with applications, with A. Lawrie and S. Shahshahani, Math. Ann. Vol. 365 (2016), no. 12, pp. 707803. arXiv:1410.5847 [math.AP] 
8  Stability of stationary equivariant wave maps from the hyperbolic plane, with A. Lawrie and S. Shahshahani, to appear in Amer. J. Math.. arXiv:1402.5981 [math.AP] 
7  Quantitative decay rates for dispersive solutions to the Einsteinscalar field system in spherical symmetry, with J. Luk, Analysis & PDE. Vol. 8 (2015), No. 7, pp. 1603–1674. arXiv:1402.2984 [grqc] 
6  Decay and scattering for the ChernSimonsSchrödinger equations, with F. Pusateri, Int. Math. Res. Not.. IMRN 2015 (2015), No. 24, pp. 1312213147 arXiv:1311.2088 [math.AP] 
5  A heat flow approach to Onsager's conjecture for the Euler equations on manifolds, with P. Isett, Trans. Amer. Math. Soc. Vol. 368 (2016), No. 9, pp. 65196537. arXiv:1310.7947 [math.AP] 
4  Finite energy global wellposedness of the ChernSimonsHiggs equations in the Coulomb gauge. arXiv:1310.3955 [math.AP] 
(The following two papers constitute a series; for an overview, see Section 1 of Paper 2.)  
3  Gauge choice for the YangMills equations using the YangMills heat flow and local wellposedness in H^{1}, J. Hyper. Diff. Equ. Vol. 11 (2014), No. 01, pp. 1 108. arXiv:1210.1558 [math.AP]. 
2  Finite Energy Global Wellposedness of the YangMills equations on $\mathbb{R}^{1+3}$: An Approach Using the YangMills Heat Flow, Duke Math. J. Vol. 164 (2015), No. 9, pp. 16691732 arXiv:1210.1557 [math.AP]. 
1  Low regularity solutions to the ChernSimonsDirac and the ChernSimonsHiggs equations in the Lorenz gauge, with H. Huh, Comm. Partial Differential Equations. Vol. 41 (2016), no. 3, 989–999. arXiv:1209.3841[math.AP] 
Expository Papers  
1  The Threshold Theorem for the (4+1)dimensional Yang–Mills equation: An overview of the proof. arXiv:1709.09088[math.AP] 
Ph.D. Thesis  
  Finite energy global wellposedness of the (3+1)dimensional YangMills equations using a novel YangMills heat flow gauge. pdf 
Previous Teaching 
In April 2017, I gave a minicourse in KIAS on General Relativity in Spherical Symmetry. 
In Spring 2015, I gave a minicourse in UC Berkeley under MAT290 (Nonlinear Hyperbolic PDEs). 
Online talks  
  Linear instability of the Cauchy horizon in subextremal ReissnerNordström 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 