Tadahiro (Choonghong) Oh


Mailing Address:
Department of Mathematics
40 St. George St, Rm 6290
Toronto, Ontario
Canada M5S 2E4

Office: BA 6103
e-mail: my_last_name 'at' math.toronto.edu

Teaching:

Fall 09:

  • APM384H1F (Partial Differential Equations)
  • Syllabus
  • Homework. (HW11 added. Will not be collected.) Also, see HW Solution (Solutions to HW 11 added.) Use HW cover sheet when you submit HW in a group.
  • TA: Geordie Richards
    --- Extra Office Hours: 1-2 pm on Dec 14 (MON) and 2-3 pm on Dec 15 (TUE) in the TA room (BA 6183.)
  • Review session: 2-4 pm on Dec 13 in BA 2145.
  • You can pick up HW 10 in front of my office. You might need to dig through the pile since there are HWs from my other course as well.
  • Final: 9:30 - 12 pm on Dec 16 in BA 2185. See Formula sheet. (It will come as the last page in the final, so do not bring a printout.)
  • HW is graded out of 80 pts. 40 pts for your part, and 10 pts for each of the other 4 parts.
  • If you have anyone in your HW group who drops/has dropped the course, you must let me know immediately.
  • MAT244H1F (Introduction to Ordinary Differential Equations)
  • Syllabus. Also, see Dilip Raghavan's website
  • MAT 244 Homework and other announcements
  • Final: 7-10 pm on Dec 16 in BN 3.
  • Teaching Assistants:
    Trefor Bazett --trefor.bazett_at_utoronto dot ca
    Steven Corkey --steven.corkey_at_utoronto.ca
    Blackboard Academic Suite
  • Fall 08
  • APM384H1F (Partial differential equations)
  • MAT196H1F (Calculus for engineers)
  • Fall 07-Spring 08
  • MAT135Y (full year course in Calculus)

  • Research Interests:

    Nonlinear Partial Differential Equations and Harmonic Analysis. In particular, study of dispersive nonlinear equations at low regularity, both in periodic and non-periodic settings, using the techniques from PDEs and nonlinear Fourier analysis. Mainly, short and long time behavior of solutions such as well-posedness (existence, uniqueness, and stability of solutions), existence of invariant Gibbs measures, etc. Also, multilinear integral operators.
    Seminars at U of T: Informal Dispersive Seminars, Fields Analysis Working Gourp, PDE/Applied Math/Analysis Seminars

    Papers:

    For published papers, please obtain copies from corresponding journals.
  • Modulation spaces, Wiener amalgam spaces, and Brownian motions (with \'A. B\'enyi).
  • Global well-posedness of the periodic stochastic KdV with multiplicative noise in L^2, completed.
  • Remarks on nonlinear smoothing under randomization for the periodic KdV and the cubic Sz\"ego equation.
  • White noise for KdV and mKdV on the circle.
  • Almost sure global solutions of the cubic nonlinear Schr\"odinger equation below L^2(T) (with J. Colliander).
  • Interpolation of the Gibbs measure and the white noise for Hamiltonian PDEs (with J. Quastel and B. Valk\'o).
  • Almost sure local well-posedness of the cubic nonlinear Schr\"odinger equation below L^2(T) (with J. Colliander).
  • Periodic stochastic Korteweg-de Vries equation with the additive space-time white noise, to appear in Anal. PDE.
  • Invariance of the white noise for KdV, Comm. Math. Phys. 292 (2009), no. 1, pp. 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''.
  • Invariance of the Gibbs measure for the Schr\"odinger-Benjamin-Ono system, SIAM J. Math. Anal. 41 (2009), no. 6, 2207-2225.
  • Invariant Gibbs measures and a.s. global well-posedness for coupled KdV systems, Diff. Integ. Equations, Vol. 22, Numbers 7-8 (2009), 637-668.
  • Diophantine conditions in global well-posedness of coupled KdV-type systems, Electron. J. Diff. Eqns., Vol. 2009 (2009), No. 52, pp. 1-48.
  • Diophantine conditions in well-posedness theory of coupled KdV-type systems: local theory, Internat. Math. Res. Not. 2009 (2009), 3516--3556.
  • Best Constants for Certain Multilinear Integral Operators, (with \'A. B\'enyi.) Journal of Inequalities and Applications, Vol. 2006 (2006), Art. ID 28582, 12 pp.
  • Book:
  • Introduction to partial differential equations, (with Y. Tsutsumi.) Translation of the book by Y. Tsutsumi from Japanese to English. 40 % completed.
  • Lecture notes:
  • Basic H^1-subcritical scattering theory: defocusing cubic NLS on R^3, Oct. 2009.
  • Weak continuity of the Wick ordered cubic NLS in L^2(T) , Oct. 2009.
  • Cauchy problem of the cubic NLS on T, Sep. 2009.
  • Invariant Gibbs measure, white noise, a.s. GWP and all that, Nov. 2008.

  • Recent Talks:

  • ''KdV with measures as initial data, and stochastic KdV with additive and multiplicative noise'', Analysis and Applied Math Seminar, University of Toronto, Toronto, Nov. 2009.
    ----Also, at York Analysis Seminar, York University, Toronto, Nov. 2009.
  • ''Basic H^1-subcritical scattering theory: defocusing cubic NLS on R^3'' (expository talk), Informal Dispersive PDE seminar University of Toronto, Toronto, Oct. 2009.
  • (Mini-course) ''Cauchy problem of the cubic NLS on T'', 2 one-and-half hour lectures, Informal Dispersive PDE seminar, University of Toronto, Toronto, Sep.-Oct. 2009.
  • ''Almost sure global solutions of the periodic cubic NLS below L^2,'' Nonlinear dispersive and geometric evolution problems: singularities and asymptotics, PIMS, Vancouver, Aug. 2009.
  • ''White noise for KdV and mKdV on the circle,'' Harmonic Analysis and Nonlinear PDEs, RIMS, Kyoto, Japan, Jul. 2009.
    ----Also, at Special Seminar, University of Toronto, Toronto, Jun. 2009.
  • ''Remarks on the white noise for 1-dimensional periodic cubic Schrodinger equation: nonlinear smoothing under randomization,'' NLPDE seminar, Kyoto University, Japan, Mar. 09.
  • ''Well-posedness of deterministic and stochastic KdV on the circle,'' NLPDE seminar, Kyoto University, Japan, Mar. 09.
  • (Mini-Course)''Invariant Gibbs measure, white noise, a.s. GWP and all that. (Part 1~3)'', Informal Seminar on Dispersive PDEs, University of Toronto, Toronto, Nov.-Dec. 08.
  • ''Multiplier problem for the ball'' (expository talk), Fields Analysis Working Group, Fields Institute, Toronto, Oct. 08. Also, at York Analysis Seminars, York University, Toronto, Oct. 08.
  • ''Invariance of the white noise for KdV and Applications'', Asymptotics and Singularities in Nonlinear and Geometric Dispersive Equations, BIRS, Banff, Aug. 08.
  • ''Invariant Gibbs measure and almost surely global well-posedness of the periodic Schrödinger-Benjamin-Ono system'', Young Mathematicians' Conference, CRM, Montreal, Jan. 08.