Walter Craig

Term 1, 2006-2007:

Mathematics 4AT: Topics in Analysis /

   Origins 3A: The origins of space and time

M 9:30 - 10:20, Tu 10:30 - 1:20, Th 9:30 - 10:20 / BSB 122

Office Hours: Tu 2:00 - 3:30 or by appointment


Course information sheet:

Syllabus:

Mathematics 748: Topics in Mathematical Physics


Syllabus - TBA

Research interests: partial differential equations and dynamical systems

Journal editorships:

   AMS, Graduate Studies in Mathematics

   Proceedings of the AMS

   Canadian Mathematical Society, Journal and Bulletin

   Fields Institute, Editorial Board

   Mathematical Physics Electronic Journal

   London Mathematical Society Monographs           

  Proceedings of the Royal Society - A: Proc. R. Soc A

Curriculum Vitae: cv.pdf file

Recent papers:

[39] ``Problèmes de petits diviseurs dans les équations aux dérivées partielles'',
Panaromas et Synthèses 9, Société Mathématiques de France (2000).

[40] ``Birkhoff normal forms for water waves'',
Mathematical problems in Water Waves,
Contemporary Math. 200 AMS (1996), pp. 57-74.

[41] ``On the microlocal regularity of the Schrödinger kernel'',
CRM Workshop on partial differential equations, Univ. Toronto June 1995.
Proceedings CRM 12 AMS (1997), pp. 71-90.

[42] ``Les moments microlocaux et la régularité des solutions de l'équation de Schrödinger'',
IHES preprint  M/96/48;
Publications du séminaire: équations aux dérivées partielles,
1995 - 1996, Ecole Polytechnique, Palaiseau, no. XX.

 - (english version) ``Microlocal moments and regularity of solutions of Schrödinger's equation'',
Math. Physics Electronic Journal 97-2 (1997), mpej@math.utexas.edu.

[43] ``Normal forms for wave motion in fluid interfaces'',
(with M. Groves), Wave Motion 31 pp. 21 - 41, (2000).

[44] ``Reheating in the presence of noise'',
(with V. Zanchin, A. Maia and R. Brandenberger), preprint hep-ph 97 09,
Physical Review D  57 (1998), pp. 4651-4662.

[45] ``Traveling two and three dimensional capillary gravity waves'',
(with D. Nicholls), SIAM: Math. Analysis  32 (2000), pp. 323-359.

[46] ``Reheating in the presence of inhomogeneous noise'',
(with V. Zanchin, A. Maia and R. Brandenberger),
preprint hep-ph 9901207,  Physical Review D 60, 023505 (1999).

[47] ``Singularities of Schrödinger equations and recurrent bicharacteristic flow'', 
Current Developments in Mathematics 1997,
International Press, Boston MA (1999), pp. 213-218.

[48] ``On the Badulin, Kharif and Shrira model of resonant water waves'',  
Physica D  2670 (2001), pp. 1-17.

[49] ``The water wave problem and its long-wave and modulational limits'',
(with C. Sulem), Fifth International Conference on `Mathematical and
Numerical Aspects of Wave Propagation', eds. A. Berm\'udez, D. Gòmez,
C. Hazard, P. Joly and J. Roberts, SIAM-INRIA, (2001) pp. 14 - 23.

[50] ``Photoacoustic point source'' (with I. Calasso and G. Diebold), 
Physical Review Letters  86 no. 16, 16 April (2001).

[51] ``The photoacoustic effect generated by heat diffusion''
(with I. Calasso & G. Diebold),  Analytical Sciences (Japan)  17,
(Proceedings of the 11'th International Conference on Photoacoustic
and Photothermal Phenomena, Kyoto) (2001), pp. s249-50.

[52] ``Traveling gravity water waves in two and three dimensions'',
(with D. Nicholls),  European J. Mech. B - Fluids  21 no. 6, (2002),
pp. 615-641.

[53] ``Nonexistence of solitary water waves in three dimensions'',
Phil. Trans. Royal Soc. London A  360 (2002), pp. 1-9. pdf-file

[54] ``Depletion layers and contact capacitance in non-uniformly doped semiconductors'',
(with A. Shik, H.E. Ruda and D. Pelinovsky),
J. Phys. D: Appl. Phys. 35 (2002), pp. 2988-2993.

[55] ``Thermal diffusion in a sinusoidal temperature field'',
(with S. Danworaphong and G. Diebold),
Phys. Rev. Letters 92, no. 12  (2004), pp. 125901-1 -- 4. pdf-file

[56] ``Sur la régularité des ondes progressives à la surface de l'eau'',
(with A.-M. Matei), Proceedings of the Groupement de recherche EDP,
Forges-les-Eaux (2003). pdf-file

[57] ``A new model for large amplitude long internal waves'',
(with P. Guyenne and H. Kalisch),
C. R. Acad. Sci. Paris  - Mecanique 332 (2004), pp. 525 - 530. pdf-file

[58] ``Hamiltonian long wave expansions for water waves  over a rough bottom'',
(with P. Guyenne, D. Nicholls and C. Sulem), Proc. Royal Society A 461, (2005), pp. 1 - 35. pdf-file

[59] ``Thermal Diffusion Shock Waves'',
(with S. Danworaphong, V. Gusev and G. Diebold)
Phys. Rev. Letters 94, p. 095901 (2005). pdf-file

[60] ``Hamiltonian long wave expansions for free surfaces and interfaces'',
(with P. Guyenne and H. Kalisch), CPAM (2005). pdf-file

[61] ``Invariant tori for Hamiltonian PDE'',
Nonlinear Dynamics and Evolution Equations,
editors: Hermann Brunner, Xiao-Qiang Zhao and Xingfu Zou,
Fields Institute Communications, AMS (2005). pdf-file

[62] ``The mathematics of thermal diffusion shocks'',
(with V. Gusev, R. LiVoti, S. Danworaphong and G. Diebold),
 Physical Review E (2005). pdf-file

[63] ``Solitary wave interactions'',
(with P. Guyenne, J. Hammack, D. Henderson and C. Sulem),
to appear in Physics of Fluids (2006). pdf-file

[64] Strong solutions of the Boltzmann equation in
one spatial dimension, (with A. Biryuk and V. Panferov),
to appear in C. R. Acad. Sci. Paris  - Mathématiques (2005).

[65] Stable three-dimensional waves of nearly permanent form
on deep water, (with D. Henderson, M. Oscamou and H. Segur),
to appear in Mathematics and Computers in Simulation (2005).

[66] On the regularity of the Neumann problem for free
surfaces with surface tension, (with A.-M. Matei),
to appear in the Proceedings AMS (2006).

[67] Solitary water wave interactions,
ICMS Workshop on Rogue Waves, December 15, 2005. pdf-file

[68] Surface water waves and tsunamis, pdf-file
J. Dynamics and Differential Equations (2006).

[69] Mathematical aspects of surface water waves, pdf-file
Workshop on mathematical hydrodynamics,
Steklov Institute Moscow June 2006.

[70] On the orbit space of the harmonic oscillator,
(with D. Haskell), in preparation.

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