### Sung-Jin Oh

#### Assistant Professor

Department of Mathematics
University of California Berkeley
Berkeley, CA, USA 94720-3840

Office: Evans Hall 887

E-mail:

I am an Assistant Professor in the Department of Mathematics at UC Berkeley.

Previously, I was a CMC Research Professor in Korea Institute for Advanced Study (KIAS) and 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
 Teaching and seminars In Fall 2020, I will be teaching Math 126 (Introduction to Partial Differential Equations).
 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, incompressible Euler equations and incompressible extended MHD equations.
 Papers & Preprints     (Click on the title to show/hide the abstract) 33 Blow-up dynamics for smooth finite energy radial data solutions to the self-dual Chern-Simons-Schrödinger equation, with S. Kwon and K. Kim. arXiv:2010.03252 [math.AP] 32 Asymptotic stability of harmonic maps on the hyperbolic plane Under the Schrödinger maps evolution, with A. Lawrie, J. Lührmann and S. Shahshahani, to appear in Comm. Pure Appl. Math. arXiv:1909.06899 [math.AP] 31 On the Cauchy problem for the Hall and electron magnetohydrodynamic equations without resistivity I: illposedness near degenerate stationary solutions, with I.-J. Jeong. arXiv:1902.02025 [math.AP] 30 Local smoothing estimates for Schrödinger equations on hyperbolic space, with A. Lawrie, J. Lührmann 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 Yang-Mills heat flow and the caloric gauge, with D. Tataru. arXiv:1709.08599 [math.AP]. 28 The hyperbolic Yang-Mills equation in the caloric gauge. Local well-posedness and control of energy dispersed solutions, with D. Tataru, Pure Appl. Anal. Vol. 2 (2020) no. 2, pp. 233-384. arXiv:1709.09332 [math.AP]. 27 The hyperbolic Yang-Mills equation for connections in an arbitrary topological class, with D. Tataru, Comm. Math. Phys. Vol. 365 (2019), no. 2, pp. 683-739. arXiv:1709.08604 [math.AP]. 26 The threshold conjecture for the energy critical hyperbolic Yang-Mills 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 two-ended asymptotically flat initial data I. The interior of the black hole region, with J. Luk, Ann. of Math. Vol. 190 (2019), no. 1, pp. 1-111. arXiv:1702.05715 [gr-qc]. 24 Strong cosmic censorship in spherical symmetry for two-ended asymptotically flat initial data II. The exterior of the black hole region, with J. Luk, Ann. PDE. Vol. 5 (2019) no. 1. arXiv:1702.05716 [gr-qc]. 23 Dynamical black holes with prescribed masses in spherical symmetry, with J. Luk and S. Yang, Proceedings of the Seventh International Congress of Chinese Mathematicians, Adv. Lect. Math., Vol. II (2019), no. 44, pp. 367-387. arXiv:1702.05717 [gr-qc]. 22 Solutions to the Einstein-scalar-field system in spherical symmetry with large bounded variation norms, with J. Luk and S. Yang, Ann. PDE. Vol. 4 (2018), no. 1, Art. 3. arXiv:1605.03893 [gr-qc]. 21 Global well-posedness of high dimensional Maxwell-Dirac for small critical data, with C. Gavrus, Mem. Amer. Math. Soc. Vol. 264 (2020), no. 1279. arXiv:1604.07900 [math.AP] 20 Small data global existence and decay for relativistic Chern-Simons equations, with M. Chae, Annales Henri Poincaré Vol 18 (2017), no. 6, 2123-2198. 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, Int. Math. Res. Not. (IMRN) 2018, no. 7, 1954-2051. 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. 725-804. preprint. 17 On the Kinetic Energy profile of Hölder continuous Euler flows, with P. Isett, Annales d'IHP (C) Vol. 34 (2017), no. 3, pp. 711-730. preprint. 16 Equivariant Wave Maps on the Hyperbolic Plane with Large Energy, with A. Lawrie and S. Shahshahani, Math. Res. Lett. Vol. 24 (2017), no. 4, 1085-1147. arXiv:1505.03728 [math.AP] (The following three papers constitute a series; for an overview, see Sections 2-3 of Paper 13.) 15 Local well-posedness of the (4+1)-dimensional Maxwell-Klein-Gordon equation, with D. Tataru, Ann. PDE. Vol. 2 (2016), No. 1. arXiv:1503.01560 [math.AP] 14 Energy dispersed large energy solutions to the (4+1) dimensional Maxwell-Klein-Gordon equation, with D. Tataru, Amer. J. Math. Vol. 140 (2018), no. 1, pp. 1-82. arXiv:1503.01561 [math.AP] 13 Finite energy global well-posedness and scattering of the (4+1) dimensional Maxwell-Klein-Gordon 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. 989-999. arXiv:1502.03435 [math.AP] 11 Gap Eigenvalues and Asymptotic Dynamics of Geometric Wave Equations on Hyperbolic Space, with A. Lawrie and S. Shahshahani, J. Funct. Anal. Vol. 271 (2016), no. 11, pp. 3111-3161. arXiv:1502.00697 [math.AP] 10 Proof of linear instability of the Reissner-Nordström Cauchy horizon under scalar perturbations, with J. Luk, Duke Math. J. Vol. 166 (2017), no. 3, pp. 437-493. arXiv:1501.04598 [gr-qc] 9 Profile decomposition for wave equations on hyperbolic space with applications, with A. Lawrie and S. Shahshahani, Math. Ann. Vol. 365 (2016), no. 1-2, pp. 707-803. arXiv:1410.5847 [math.AP] 8 Stability of stationary equivariant wave maps from the hyperbolic plane, with A. Lawrie and S. Shahshahani, Amer. J. Math. Vo. 139 (2017), no. 4, pp. 1085-1147. arXiv:1402.5981 [math.AP] 7 Quantitative decay rates for dispersive solutions to the Einstein-scalar field system in spherical symmetry, with J. Luk, Analysis & PDE. Vol. 8 (2015), No. 7, pp. 1603–1674. arXiv:1402.2984 [gr-qc] 6 Decay and scattering for the Chern-Simons-Schrödinger equations, with F. Pusateri, Int. Math. Res. Not.. IMRN 2015 (2015), No. 24, pp. 13122-13147 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. 6519-6537. arXiv:1310.7947 [math.AP] 4 Finite energy global well-posedness of the Chern-Simons-Higgs 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 Yang-Mills equations using the Yang-Mills heat flow and local well-posedness in H^{1}, J. Hyper. Diff. Equ. Vol. 11 (2014), No. 01, pp. 1- 108. arXiv:1210.1558 [math.AP]. 2 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 (2015), No. 9, pp. 1669-1732 arXiv:1210.1557 [math.AP]. 1 Low regularity solutions to the Chern-Simons-Dirac and the Chern-Simons-Higgs 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     (Click on the title to show/hide the abstract) 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     (Click on the title to show/hide the abstract) - Finite energy global well-posedness of the (3+1)-dimensional Yang-Mills equations using a novel Yang-Mills heat flow gauge. pdf
 Previous Teaching In Spring 2019, I organized an informal reading seminar on singularity formation in incompressible fluids. In Fall 2019, I taught Math 222A (Partial Differential Equations) and Math 278 (Topics in Analysis: General Relativity in Spherical Symmetry). In April 2017, I gave a mini-course in KIAS on General Relativity in Spherical Symmetry. In Spring 2015, I gave a mini-course in UC Berkeley 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 3 Lecture notes for Math 222A (Based on MATH 222 at UC Berkeley, Fall 2019) pdf 2 Lecture notes on linear wave equation. (Based on guest lectures in MATH 222 at UC Berkeley, Fall 2014) pdf 1 Counterexample for sharp trace theorem. pdf