James Colliander

James Ellis Colliander (born 22 June 1967) is an American-Canadian mathematician. He is currently Professor of Mathematics at University of British Columbia and serves as Director of the Pacific Institute for the Mathematical Sciences. Colliander is also the Founder of an education technology company called Crowdmark. He was born in El Paso, Texas, and lived there until age 8 and then moved to Hastings, Minnesota. He graduated from Macalester College in 1989. He worked for two years at the United States Naval Research Laboratory on fiber optic sensors and then went to graduate school to study mathematics. He received his PhD from the University of Illinois at Urbana–Champaign in 1997 and was advised by Jean Bourgain. Colliander was a postdoctoral fellow at the University of California, Berkeley and spent semesters at the University of Chicago, the Institute for Advanced Study and the 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, especially non-linear Schrödinger equation.^[2]

Colliander is a collaborator with Markus Keel, Gigliola Staffilani, Hideo Takaoka, and 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 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 citations for group member Tao.^[4][6]

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 ${\displaystyle \mathbb {R} }$ and ${\displaystyle \mathbb {T} }$. 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 ${\displaystyle \mathbb {R} ^{3}}$. Comm. Pure Appl. Math. 57 (2004), no. 8, 987–1014.
• Colliander, J.; Keel, M.; Staffilani, G.; Takaoka, H.; Tao, T. Global well-posedness and scattering for the energy-critical nonlinear Schrödinger equation in ${\displaystyle \mathbb {R} ^{3}}$. Ann. of Math. (2) 167 (2008), no. 3, 767–865. doi:10.4007/annals.2008.167.767 MR2415387

References[]

External links[]

• Official website
• MathSciNet: "Items authored by Colliander, James."^{[permanent dead link]}
• James Colliander at the Mathematics Genealogy Project
• James Colliander introducing Crowdmark at 2013 Launch Education and Kids on YouTube
• James Colliander publications indexed by Google Scholar