Tadahiro (Choonghong) Oh

Teaching:

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

APM384H1F (Partial differential equations)

MAT196H1F (Calculus for engineers)

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:

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.

Introduction to partial differential equations, (with Y. Tsutsumi.) Translation of the book by Y. Tsutsumi from Japanese to English. 40 % completed.

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.