
SungJin OhMiller Research Fellow Department of Mathematics Office: 887 Evans Hall Email: 
I have moved to Korea Institute for Advanced Study.

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  
1  Solutions to the Einsteinscalarfield system in spherical symmetry with large bounded variation norms, with J. Luk and S. Yang. arXiv:1605.03893 [grqc]. 
2  Global wellposedness of high dimensional MaxwellDirac for small critical data, with C. Gavrus. arXiv:1604.07900 [math.AP] 
3  Small data global existence and decay for relativistic ChernSimons 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 wellposedness of the (4+1)dimensional MaxwellKleinGordon 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 MaxwellKleinGordon equation, with D. Tataru, to appear in Amer. J. Math. arXiv:1503.01561 [math.AP] 
10  Finite energy global wellposedness and scattering of the (4+1) dimensional MaxwellKleinGordon 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 ReissnerNordström Cauchy horizon under scalar perturbations, with J. Luk, to appear in Duke Math. J. arXiv:1501.04598 [grqc] 
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 Einsteinscalar field system in spherical symmetry, with J. Luk, Analysis & PDE. Vol. 8, No. 7 (2015), pp. 1603–1674. arXiv:1402.2984 [grqc] 
17  Decay and scattering for the ChernSimonsSchrödinger 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 wellposedness of the ChernSimonsHiggs equations in the Coulomb gauge. arXiv:1310.3955 [math.AP] 
20  Gauge choice for the YangMills equations using the YangMills heat flow and local wellposedness in H^{1}, J. Hyper. Diff. Equ. Vol. 11, No. 01, pp. 1 108. arXiv:1210.1558 [math.AP]. 
21  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, No. 9 (2015), pp. 16691732 arXiv:1210.1557 [math.AP]. 
22  Low regularity solutions to the ChernSimonsDirac and the ChernSimonsHiggs 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 wellposedness of the (3+1)dimensional YangMills equations using a novel YangMills heat flow gauge. pdf 
Teaching 
In Spring 2015, I gave a minicourse 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 