Tadahiro (Choonghong) Oh
  • Chancellor's Fellow What is a Chancellor's Fellow?   &   Reader = tenured associate professor
  • Mailing Address:
    School of Mathematics
    The University of Edinburgh
    James Clerk Maxwell Building, Rm 4609
    The King's Buildings, Peter Guthrie Tait Road
    Edinburgh, EH9 3FD, United Kingdom

    Office: Rm 4609 JCMB
    e-mail: hiro.oh ed.ac.uk

        duck or rabbit?

        Oct. 2007
    Also, niece & nephew, Aug. 2014
    Mar. 2013, Oct. 2012, Dec. 2011

    Research | Brief CV | Publications | Talks | Teaching | Links

    Want to learn how to count? Cute movie on "Combinatorial Explosion" by National Museum of Emerging Science and Innovation in Japan


    Maxwell Institute Graduate School in Analysis and its Applications (MIGSAA): Visit this website

    Projects by first year Ph.D. students in MIGSAA:   2015,   2016 no1,  2016 no2,   2017 no1,   2017 no2


    Teaching: Staff mail at UoE Academic CalendarMath info siteEASELearnPurePATH
       
                   
     Spring 18:   Nonlinear Schrödinger Equations (MATH11137), Dispersive Equations (MIGSAA advanced Ph.D. course): Course webpage
    tutorials for Fundamentals of Pure Mathematics (FPM, MATH08064)
     Fall 17:   tutorials for Honours Differential Equations (HDEq, MATH10066)
     Spring 17:
     
    Probabilistic Perspectives in Nonlinear Dispersive PDEs (MIGSAA advanced Ph.D. course): Course webpage
    tutorials for Fundamentals of Pure Mathematics (FPM, MATH08064)
     Fall 16:   tutorials for Honours Differential Equations (HDEq, MATH10066, 2 sections)
     Spring 16:
     
    Nonlinear Schrödinger Equations (MATH11137), Dispersive Equations (MIGSAA advanced Ph.D. course): Course webpage
    tutorials for Fundamentals of Pure Mathematics (FPM, MATH08064, 2 sections)
     Fall 14: Introduction to Linear Algebra (ILA, MATH08057)
    tutorials for ILA (3 sections), Facets of Mathematics (MATH08068)
     Spring 14: tutorials for Proofs and Problem Solving (PPS, MATH08059, two-hour tutorial), Fourier Analysis (MATH10058), Honours Analysis (MATH10068, one-hour tutorial + two-hour Skills workshop)
     Fall 13:tutorials for Introduction to Linear Algebra (ILA, MATH08057, 2 sections), Accelerated Proofs and Problem Solving (APPS, MATH08071), Hilbert spaces (MATH10046)

    Research Interest: Analysis group at UoE
    Nonlinear Partial Differential Equations and Harmonic Analysis. In particular, study of (deterministic and stochastic) nonlinear dispersive Hamiltonian PDEs, using the techniques from PDEs, nonlinear Fourier analysis, and probability. Mainly, short and long time behavior of solutions such as well-posedness (existence, uniqueness, and stability of solutions) in both deterministic and probabilistic settings, existence of invariant measures and their properties, solitons, growth of higher Sobolev norms related to weak turbulence, etc. Also, interested in multilinear integral/pseudodifferential operators.
    Seminars:Analysis Seminar,   UoE seminars,   MI events,   ICMS events, London Analysis and Probability Seminar,   Paris-London Analysis Seminar

    Papers:

    For published papers, please obtain copies from corresponding journals. Preprints on arXiv may not be up-to-date.
    1. (with J. Forlano, Y. Wang) Stochastic cubic nonlinear Schrödinger equation with almost space-time white noise.
    2. (with O. Pocovnicu, Y. Wang) On the stochastic nonlinear Schrödinger equations with non-smooth additive noise.
    3. (with S. Kwon, H. Yoon) Normal form approach to unconditional well-posedness of nonlinear dispersive PDEs on the real line.
    4. (with Á. Bényi, O. Pocovnicu) On the probabilistic Cauchy theory for nonlinear dispersive PDEs, to appear in Landscapes of Time-Frequency Analysis, Appl. Numer. Harmon. Anal., Birkhäuser/Springer.
    5. (with Y. Tsutsumi, N. Tzvetkov) Quasi-invariant Gaussian measures for the cubic nonlinear Schrödinger equation with third order dispersion.
    6. (with Á. Bényi, O. Pocovnicu) Higher order expansions for the probabilistic local Cauchy theory of the cubic nonlinear Schrödinger equation on ℝ3.
    7. (with N. Tzvetkov, Y. Wang) Solving the 4NLS with white noise initial data.
    8. (with M. Okamoto, O. Pocovnicu) On the probabilistic well-posedness of the nonlinear Schrödinger equations with non-algebraic nonlinearities.
    9. (with N. Tzvetkov) Quasi-invariant Gaussian measures for the two-dimensional defocusing cubic nonlinear wave equation, to appear in J. Eur. Math. Soc.
    10. (with Y. Wang) Global well-posedness of the periodic cubic fourth order NLS in negative Sobolev spaces (arXiv link), Forum Math. Sigma 6 (2018), e5, 80 pp.
    11. (with L. Thomann) Invariant Gibbs measures for the 2-d defocusing nonlinear wave equations, to appear in Ann. Fac. Sci. Toulouse Math.
    12. (with M. Gubinelli, H. Koch) Renormalization of the two-dimensional stochastic nonlinear wave equations, to appear in Trans. Amer. Math. Soc.
    13. (with P. Sosoe, N. Tzvetkov) An optimal regularity result on the quasi-invariant Gaussian measures for the cubic fourth order nonlinear Schrödinger equation.
    14. (with N. Tzvetkov) On the transport of Gaussian measures under the flow of Hamiltonian PDEs, Séminaire Laurent Schwartz--Équations aux dérivées partielles et applications. Année 2015--2016, Exp. No. VI, 9 pp., Ed. Éc. Polytech., Palaiseau, 2017.
    15. A remark on norm inflation with general initial data for the cubic nonlinear Schrödinger equations in negative Sobolev spaces, Funkcial. Ekvac. 60 (2017) 259--277.
    16. (with G. Richards, L. Thomann) On invariant Gibbs measures for the generalized KdV equations, Dyn. Partial Differ. Equ. 13 (2016), no.2, 133--153.
    17. (with Y. Wang) On the ill-posedness of the cubic nonlinear Schrödinger equation on the circle, to appear in An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat. (N.S.)
    18. (with J. Chung, Z. Guo, S. Kwon) Normal form approach to global well-posedness of the quadratic derivative nonlinear Schrödinger equation on the circle, Ann. Inst. H. Poincaré Anal. Non Linéaire 34 (2017), 1273--1297.
    19. (with N. Tzvetkov) Quasi-invariant Gaussian measures for the cubic fourth order nonlinear Schrödinger equation (arXiv link), Probab. Theory Related Fields 169 (2017), 1121--1168.
    20. (with O. Pocovnicu) A remark on almost sure global well-posedness of the energy-critical defocusing nonlinear wave equations in the periodic setting, Tohoku Math. J. 69 (2017), no.3, 455--481.
    21. (with L. Thomann) A pedestrian approach to the invariant Gibbs measure for the 2-d defocusing nonlinear Schrödinger equations (arXiv link), Stoch. Partial Differ. Equ. Anal. Comput. (2018) https://doi.org/10.1007/s40072-018-0112-2
    22. (with O. Pocovnicu) Probabilistic global well-posedness of the energy-critical defocusing quintic nonlinear wave equation on ℝ3, J. Math. Pures Appl. 105 (2016), 342--366.
    23. (with R. Mosincat) A remark on global well-posedness of the derivative nonlinear Schrödinger equation on the circle, C. R. Math. Acad. Sci. Paris. 353 (2015), no. 9, 837--841.
    24. (with Á. Bényi) Linear and bilinear T(b) theorems à la Stein, Proc. Amer. Math. Soc. Ser. B 2 (2015), 1--16.
    25. (with Z. Guo) Non-existence of solutions for the periodic cubic nonlinear Schrödinger equation below L2, Internat. Math. Res. Not. 2018, no.6, 1656--1729.
    26. Global existence for the defocusing nonlinear Schrödinger equations with limit periodic initial data, Commun. Pure Appl. Anal. 14 (2015), no. 4, 1563--1580.
    27. (with J. Quastel, P. Sosoe) Invariant Gibbs measures for the defocusing nonlinear Schrödinger equations on the real line.
    28. On nonlinear Schrödinger equations with almost periodic initial data, SIAM J. Math. Anal. 47 (2015), no. 2, 1253--1270.
    29. (with Á. Bényi, O. Pocovnicu) On the probabilistic Cauchy theory of the cubic nonlinear Schrödinger equation on ℝd, d ≥ 3 (arXiv link), Trans. Amer. Math. Soc. Ser. B 2 (2015), 1--50.
    30. (with Á. Bényi, O. Pocovnicu) Wiener randomization on unbounded domains and an application to almost sure well-posedness of NLS, Excursions in harmonic analysis. Vol. 4, 3--25, Appl. Numer. Harmon. Anal., Birkhäuser/Springer, Cham, 2015.
    31. (with Z. Guo, Y. Wang) Strichartz estimates for Schrödinger equations on irrational tori, Proc. Lond. Math. Soc. (3) 109 (2014), no. 4, 975--1013. doi: 10.1112/plms/pdu025.
    32. (with Á. Bényi) Smoothing of commutators for a Hörmander class of bilinear pseudodifferential operators, J. Fourier Anal. Appl. 20 (2014), no. 2, 282--300.
    33. (with J. Quastel) On Cameron-Martin theorem and almost sure global existence, Proc. Edinb. Math. Soc. 59 (2016), 483--501.
    34. (with R. Killip, O. Pocovnicu, M. Vişan) Solitons and scattering for the cubic-quintic nonlinear Schrödinger equation on ℝ3, Arch. Ration. Mech. Anal. 225 (2017), no. 1, 469--548.
    35. (with Á. Bényi) On a class of bilinear pseudodifferential operators, J. Funct. Spaces Appl. vol. 2013, Article ID 560976, 5 pp, 2013. doi:10.1155/2013/560976.
    36. (with J. Colliander, J. Marzuola, G. Simpson) Behavior of a model dynamical system with applications to weak turbulence, Exp. Math. 22 (2013), no. 3, 250--264.
    37. A blowup result for the periodic NLS without gauge invariance, C. R. Math. Acad. Sci. Paris 350 (2012), no. 7--8, 389--392.
    38. (with R. Killip, O. Pocovnicu, M. Vişan) Global well-posedness of the Gross-Pitaevskii and cubic-quintic nonlinear Schrödinger equations with non-vanishing boundary conditions, Math. Res. Lett. 19 (2012), no. 5, 969--986.
    39. (with Á. Bényi) The Sobolev inequality on the torus revisited, Publ. Math. Debrecen 83 (2013), no. 3, 359--374.
    40. (with Z. Guo, S. Kwon) Poincaré-Dulac normal form reduction for unconditional well-posedness of the periodic cubic NLS, Comm. Math. Phys. 322 (2013), no.1, 19--48.
    41. (with J. Quastel) On invariant Gibbs measures conditioned on mass and momentum, J. Math. Soc. Japan 65 (2013), no. 1, 13--35.
    42. (with J. Colliander, S. Kwon) A remark on normal forms and the "upside-down" I-method for periodic NLS: growth of higher Sobolev norms, J. Anal. Math. 118 (2012), 55--82.
    43. (with A. Nahmod, L. Rey-Bellet, G. Staffilani) Invariant weighted Wiener measures and almost sure global well-posedness for the periodic derivative NLS, J. Eur. Math. Soc. 14 (2012), 1275--1330.
    44. (with S. Kwon) On unconditional well-posedness of modified KdV, Internat. Math. Res. Not. 2012, no. 15, 3509--3534.
    45. (with C. Sulem) On the one-dimensional cubic nonlinear Schrödinger equation below L2, Kyoto J. Math. 52 (2012), no.1, 99--115.
    46. (with Á. Bényi) Modulation spaces, Wiener amalgam spaces, and Brownian motions, Adv. Math. 228 (2011), no. 5, 2943--2981.
    47. Remarks on nonlinear smoothing under randomization for the periodic KdV and the cubic Szegö equation, Funkcial. Ekvac. 54 (2011), no. 3, 335--365.
    48. White noise for KdV and mKdV on the circle, Harmonic analysis and nonlinear partial differential equations, 99--124, RIMS Kôkyûroku Bessatsu, B18, Res. Inst. Math. Sci. (RIMS), Kyoto, 2010.
    49. (with J. Quastel, B. Valkó) Interpolation of Gibbs measures and white noise for Hamiltonian PDE, J. Math. Pures Appl. 97 (2012), no. 4, 391--410.
    50. (with J. Colliander) Almost sure well-posedness of the cubic nonlinear Schrödinger equation below L2(𝕋), Duke Math. J. 161 (2012), no. 3, 367--414.
    51. Periodic stochastic Korteweg-de Vries equation with additive space-time white noise, Anal. PDE 2 (2009), no. 3, 281--304.
    52. Invariance of the white noise for KdV, Comm. Math. Phys. 292 (2009), no. 1, 217--236. Also, see Erratum: Invariance of the white noise for KdV, in preparation. For the correct nonlinear analysis, please see ''White noise for KdV and mKdV on the circle''.
    53. Invariance of the Gibbs measure for the Schrödinger-Benjamin-Ono system, SIAM J. Math. Anal. 41 (2009/10), no. 6, 2207--2225.
    54. Invariant Gibbs measures and a.s. global well-posedness for coupled KdV systems, Differential Integral Equations 22 (2009), no. 7--8, 637--668.
    55. Diophantine conditions in global well-posedness of coupled KdV-type systems, Electron. J. Differential Equations 2009, no. 52, 48 pp.
    56. Diophantine conditions in well-posedness theory of coupled KdV-type systems: local theory, Int. Math. Res. Not. 2009, no. 18, 3516--3556.
    57. (with Á. Bényi) Best Constants for Certain Multilinear Integral Operators, J. Inequal. Appl. 2006, Art. ID 28582, 12 pp.
    Book: Notes:

    Ph.D. Students:

    Posdocs:

    • Dimitrios Roxanas (University of Edinburgh, since 2017).
    • Yuzhao Wang (University of Edinburgh, 2016-2017).
    • Oana Pocovnicu (Princeton University, 2012-2013).


    Links: