James Colliander

Colliander's research mostly addresses dynamical aspects of solutions of Hamiltonian partial differential equations, especially non-linear Schrödinger equation.{{harvtxt|Colliander|Keel|Staffilani|Takaoka|2008}}; {{harvtxt|Colliander|Keel|Staffilani|Takaoka|2010}}.

Colliander is a collaborator with Markus Keel, Gigliola Staffilani, Hideo Takaoka, and Terence Tao, forming a group known as the "I-team".{{citation|url=http://www.siam.org/news/news.php?id=1963|title=Quello Che Si Far per Amore? Della Matematica|date=18 March 2012|department=Careers in the Math Sciences|first=Gigliola|last=Staffilani|access-date=2 January 2015|archive-url=https://web.archive.org/web/20180401065345/http://www.siam.org/news/news.php?id=1963|archive-date=1 April 2018|url-status=dead}}.{{citation|contribution-url=http://www.icm2006.org/proceedings/Vol_I/7.pdf|title=International Congress of Mathematicians|year=2006|contribution=The work of Terence Tao|first=Charles|last=Fefferman|authorlink=Charles Fefferman|access-date=2 January 2015|archive-date=9 August 2011|archive-url=https://web.archive.org/web/20110809081829/http://www.icm2006.org/proceedings/Vol_I/7.pdf|url-status=dead}}. The name of this group has been said to come from a mollification operator used in the team's method of almost conserved quantities,[https://web.archive.org/web/20120925081237/http://wiki.math.toronto.edu/DispersiveWiki/index.php/I-method I-method], Dispersive Wiki, retrieved 2015-01-02. or as an abbreviation for "interaction", referring both to the teamwork of the group and to the interactions of light waves with each other.[http://www.icm2006.org/dailynews/fields_tao_info_en.pdf Fields Medal announcement for Terry Tao] {{Webarchive|url=https://web.archive.org/web/20160303230201/http://www.icm2006.org/dailynews/fields_tao_info_en.pdf |date=3 March 2016 }}, International Congress of Mathematicians, 2006, retrieved 2015-01-02. The group's work was featured in the 2006 Fields Medal citations for group member Tao.

Colliander is co-founder of the education technology company called [https://crowdmark.com Crowdmark].

Colliander, with colleagues from PIMS, created [https://syzygy.ca/ Syzygy], a project that provides interactive computing for students and teachers at universities across Canada. Syzygy operates on infrastructure provided by Compute Canada.

Colliander, with colleagues from PIMS and Cybera, created [https://callysto.ca Callysto], a project designed to improve computational thinking for students and teachers in grades 5-12.

Colliander is co-founder of the [https://2i2c.org International Interactive Computing Collaboration (2i2c)].

• Colliander, J.; Keel, M.; Staffilani, G.; Takaoka, H.; Tao, T. Global well-posedness for Schrödinger equations with derivative. SIAM J. Math. Anal. 33 (2001), no. 3, 649–669.
• Colliander, J.; Keel, M.; Staffilani, G.; Takaoka, H.; Tao, T. A refined global well-posedness result for Schrödinger equations with derivative. SIAM J. Math. Anal. 34 (2002), no. 1, 64–86.
• Colliander, J.; Keel, M.; Staffilani, G.; Takaoka, H.; Tao, T. Almost conservation laws and global rough solutions to a nonlinear Schrödinger equation. Math. Res. Lett. 9 (2002), no. 5-6, 659–682.
• Christ, Michael; Colliander, James; Tao, Terence. Asymptotics, frequency modulation, and low regularity ill-posedness for canonical defocusing equations. Amer. J. Math. 125 (2003), no. 6, 1235–1293.
• Colliander, J.; Keel, M.; Staffilani, G.; Takaoka, H.; Tao, T. Sharp global well-posedness for KdV and modified KdV on $\backslash mathbb\{R\}$ and $\backslash mathbb\{T\}$. J. Amer. Math. Soc. 16 (2003), no. 3, 705–749.
• Colliander, J.; Keel, M.; Staffilani, G.; Takaoka, H.; Tao, T. Multilinear estimates for periodic KdV equations, and applications. J. Funct. Anal. 211 (2004), no. 1, 173–218.
• Colliander, J.; Keel, M.; Staffilani, G.; Takaoka, H.; Tao, T. Global existence and scattering for rough solutions of a nonlinear Schrödinger equation on $\backslash mathbb\{R\}^3$. Comm. Pure Appl. Math. 57 (2004), no. 8, 987–1014.
• {{citation |last1=Colliander |first1=J. |last2=Keel |first2=M. |last3=Staffilani |first3=G. |author3-link=Gigliola Staffilani |last4=Takaoka |first4=H. |last5=Tao |first5=T. |author5-link=Terence Tao |doi=10.4007/annals.2008.167.767 |issue=3 |journal=Annals of Mathematics |mr=2415387 |pages=767–865 |series=Second Series |title=Global well-posedness and scattering for the energy-critical nonlinear Schrödinger equation in ℝ³ |volume=167 |year=2008|doi-access=free }}.
• {{citation |last1=Colliander |first1=J. |last2=Keel |first2=M. |last3=Staffilani |first3=G. |author3-link=Gigliola Staffilani |last4=Takaoka |first4=H. |last5=Tao |first5=T. |author5-link=Terence Tao |doi=10.1007/s00222-010-0242-2 |issue=1 |journal=Inventiones Mathematicae |mr=2651381 |pages=39–113 |title=Transfer of energy to high frequencies in the cubic defocusing nonlinear Schrödinger equation |volume=181 |year=2010|doi-access=free |bibcode=2010InMat.181...39C |hdl=1721.1/71665 |hdl-access=free }}.

{{Reflist}}

• {{Official website|http://colliand.com}}
• {{MathGenealogy|id=63499}}
• {{YouTube|z9XM4fyY3z4|James Colliander introducing Crowdmark at 2013 Launch Education and Kids}}
• {{GoogleScholar|CioUdggAAAAJ}}

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Category:1967 births

Category:Living people

Category:Mathematical analysts

Category:Academic staff of the University of British Columbia Faculty of Science

Category:20th-century American mathematicians

Category:21st-century American mathematicians

Category:Canadian mathematicians

Category:University of Illinois Urbana-Champaign alumni