# James Colliander

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**James Ellis Colliander** (born 22 June 1967) is an American-[Canadian](/source/Canadians) [mathematician](/source/Mathematician). He is currently Professor of Mathematics at [University of British Columbia](/source/University_of_British_Columbia) and served as Director of the [Pacific Institute for the Mathematical Sciences](/source/Pacific_Institute_for_the_Mathematical_Sciences) (PIMS) during 2016-2021. He was born in [El Paso, Texas](/source/El_Paso,_Texas), and lived there until age 8 and then moved to [Hastings, Minnesota](/source/Hastings,_Minnesota). He graduated from [Macalester College](/source/Macalester_College) in 1989. He worked for two years at the [United States Naval Research Laboratory](/source/United_States_Naval_Research_Laboratory) on [fiber optic sensors](/source/Fiber_optic_sensor) and then went to graduate school to study mathematics. He received his PhD from the [University of Illinois at Urbana–Champaign](/source/University_of_Illinois_at_Urbana%E2%80%93Champaign) in 1997 and was advised by [Jean Bourgain](/source/Jean_Bourgain). Colliander was a postdoctoral fellow at the [University of California, Berkeley](/source/University_of_California,_Berkeley) and spent semesters at the University of Chicago, the [Institute for Advanced Study](/source/Institute_for_Advanced_Study) and the [Mathematical Sciences Research Institute](/source/Mathematical_Sciences_Research_Institute).

He is also an award-winning teacher.[1]

## Research

Colliander's research mostly addresses dynamical aspects of solutions of Hamiltonian [partial differential equations](/source/Partial_differential_equations), especially [non-linear Schrödinger equation](/source/Non-linear_Schr%C3%B6dinger_equation).[2]

Colliander is a collaborator with Markus Keel, [Gigliola Staffilani](/source/Gigliola_Staffilani), Hideo Takaoka, and [Terence Tao](/source/Terence_Tao), forming a group known as the "I-team".[3][4] The name of this group has been said to come from a mollification [operator](/source/Operator_(mathematics)) used in the team's *method of almost conserved quantities*,[5] or as an abbreviation for "interaction", referring both to the teamwork of the group and to the interactions of light waves with each other.[6] The group's work was featured in the 2006 [Fields Medal](/source/Fields_Medal) citations for group member Tao.[4][6]

## Organization creation

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

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

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

## Major publications

- 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 \mathbb{R} and \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 \mathbb{R}^3. Comm. Pure Appl. Math. 57 (2004), no. 8, 987–1014.
- Colliander, J.; Keel, M.; Staffilani, G.; Takaoka, H.; Tao, T. (2008), "Global well-posedness and scattering for the energy-critical nonlinear Schrödinger equation in ℝ3", *[Annals of Mathematics](/source/Annals_of_Mathematics)*. **167** (3): 767–865, Second Series, [doi:10.4007/annals.2008.167.767](https://doi.org/10.4007/annals.2008.167.767). MR 2415387.
- Colliander, J.; Keel, M.; Staffilani, G.; Takaoka, H.; Tao, T. (2010), "Transfer of energy to high frequencies in the cubic defocusing nonlinear Schrödinger equation", *[Inventiones Mathematicae](/source/Inventiones_Mathematicae)*. **181** (1): 39–113, [Bibcode:2010InMat.181...39C](https://ui.adsabs.harvard.edu/abs/2010InMat.181...39C). [doi:10.1007/s00222-010-0242-2](https://doi.org/10.1007/s00222-010-0242-2). [hdl:1721.1/71665](https://hdl.handle.net/1721.1/71665). MR 2651381.

## References

1. [Newsletter](http://www.artsci.utoronto.ca/main/newsitems/march-2-2010-2014-colliander-wins-outstanding-teaching-award) of [University of Toronto Faculty of Arts and Science](/source/University_of_Toronto_Faculty_of_Arts_and_Science) ([Archived](https://web.archive.org/web/20181002143357/http://www.artsci.utoronto.ca/main/newsitems/march-2-2010-2014-colliander-wins-outstanding-teaching-award) 2 October 2018 at the Wayback Machine)

1. Colliander et al. (2008); Colliander et al. (2010).

1. Staffilani, Gigliola (18 March 2012), ["Quello Che Si Far per Amore? Della Matematica"](https://web.archive.org/web/20180401065345/http://www.siam.org/news/news.php?id=1963), archived from [the original](http://www.siam.org/news/news.php?id=1963) on 1 April 2018, retrieved 2 January 2015.

1. Fefferman, Charles (2006), ["The work of Terence Tao"](https://web.archive.org/web/20110809081829/http://www.icm2006.org/proceedings/Vol_I/7.pdf), "[International Congress of Mathematicians](/source/International_Congress_of_Mathematicians)", archived from [the original](http://www.icm2006.org/proceedings/Vol_I/7.pdf) on 9 August 2011, retrieved 2 January 2015.

1. [I-method](https://web.archive.org/web/20120925081237/http://wiki.math.toronto.edu/DispersiveWiki/index.php/I-method), Dispersive Wiki, retrieved 2015-01-02.

1. [Fields Medal announcement for Terry Tao](http://www.icm2006.org/dailynews/fields_tao_info_en.pdf) [Archived](https://web.archive.org/web/20160303230201/http://www.icm2006.org/dailynews/fields_tao_info_en.pdf) 3 March 2016 at the Wayback Machine, [International Congress of Mathematicians](/source/International_Congress_of_Mathematicians), 2006, retrieved 2015-01-02.

## External links

- [Official website](http://colliand.com)
- [James Colliander introducing Crowdmark at 2013 Launch Education and Kids](https://www.youtube.com/z9XM4fyY3z4) on YouTube

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