James Colliander
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James Ellis Colliander (born 22 June 1967) is an American-
Canadian Canadians () are people identified with the country of Canada. This connection may be residential, legal, historical or cultural. For most Canadians, many (or all) of these connections exist and are collectively the source of their being ''C ...
mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
. He is currently Professor of Mathematics at
University of British Columbia The University of British Columbia (UBC) is a Public university, public research university with campuses near University of British Columbia Vancouver, Vancouver and University of British Columbia Okanagan, Kelowna, in British Columbia, Canada ...
and served as Director of the Pacific Institute for the Mathematical Sciences (PIMS) during 2016-2021. He was born in
El Paso, Texas El Paso (; ; or ) is a city in and the county seat of El Paso County, Texas, United States. The 2020 United States census, 2020 population of the city from the United States Census Bureau, U.S. Census Bureau was 678,815, making it the List of ...
, and lived there until age 8 and then moved to
Hastings, Minnesota Hastings ( ) is a city mostly in Dakota County, Minnesota, Dakota County, Minnesota, of which it is the county seat, with a portion in Washington County, Minnesota, Washington County, Minnesota, United States. It is near the confluence of the M ...
. He graduated from
Macalester College Macalester College ( ) is a private liberal arts college in Saint Paul, Minnesota, United States. Founded in 1874, Macalester is exclusively an undergraduate institution with an enrollment of 2,142 students in the fall of 2023. The college ha ...
in 1989. He worked for two years at the
United States Naval Research Laboratory The United States Naval Research Laboratory (NRL) is the corporate research laboratory for the United States Navy and the United States Marine Corps. Located in Washington, DC, it was founded in 1923 and conducts basic scientific research, appl ...
on
fiber optic sensor A fiber-optic sensor is a sensor that uses optical fiber either as the sensing element ("intrinsic sensors"), or as a means of relaying signals from a remote sensor to the electronics that process the signals ("extrinsic sensors"). Fibers have m ...
s and then went to graduate school to study mathematics. He received his PhD from the
University of Illinois at Urbana–Champaign The University of Illinois Urbana-Champaign (UIUC, U of I, Illinois, or University of Illinois) is a public land-grant research university in the Champaign–Urbana metropolitan area, Illinois, United States. Established in 1867, it is the f ...
in 1997 and was advised by
Jean Bourgain Jean Louis, baron Bourgain (; – ) was a Belgian mathematician. He was awarded the Fields Medal in 1994 in recognition of his work on several core topics of mathematical analysis such as the geometry of Banach spaces, harmonic analysis, ergodi ...
. Colliander was a postdoctoral fellow at the
University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California), is a Public university, public Land-grant university, land-grant research university in Berkeley, California, United States. Founded in 1868 and named after t ...
and spent semesters at the University of Chicago, the
Institute for Advanced Study The Institute for Advanced Study (IAS) is an independent center for theoretical research and intellectual inquiry located in Princeton, New Jersey. It has served as the academic home of internationally preeminent scholars, including Albert Ein ...
and the
Mathematical Sciences Research Institute The Simons Laufer Mathematical Sciences Institute (SLMath), formerly the Mathematical Sciences Research Institute (MSRI), is an independent nonprofit mathematical research institution on the University of California campus in Berkeley, Califor ...
. He is also an award-winning teacher.


Research

Colliander's research mostly addresses dynamical aspects of solutions of Hamiltonian
partial differential equations In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives. The function is often thought of as an "unknown" that solves the equation, similar to how ...
, especially
non-linear Schrödinger equation In mathematics and science, a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathem ...
. Colliander is a collaborator with Markus Keel, Gigliola Staffilani, Hideo Takaoka, and
Terence Tao Terence Chi-Shen Tao (; born 17 July 1975) is an Australian-American mathematician, Fields medalist, and professor of mathematics at the University of California, Los Angeles (UCLA), where he holds the James and Carol Collins Chair in the Co ...
, forming a group known as the "I-team".. The name of this group has been said to come from a mollification
operator Operator may refer to: Mathematics * A symbol indicating a mathematical operation * Logical operator or logical connective in mathematical logic * Operator (mathematics), mapping that acts on elements of a space to produce elements of another sp ...
used in the team's ''method of almost conserved quantities'',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.Fields Medal announcement for Terry Tao
,
International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the IMU Abacus Medal (known before ...
, 2006, retrieved 2015-01-02.
The group's work was featured in the 2006
Fields Medal The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of Mathematicians, International Congress of the International Mathematical Union (IMU), a meeting that takes place e ...
citations for group member Tao.


Organization creation

Colliander is co-founder of the education technology company calle
Crowdmark
Colliander, with colleagues from PIMS, create
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 Cybera is a not-for-profit corporation responsible for the operation of Alberta's Optical Regional Advanced Network. This network, known as CyberaNet, connects Alberta's research universities, colleges, K-12 schools, not-for-profits, and busines ...
, create
Callysto
a project designed to improve computational thinking for students and teachers in grades 5-12. Colliander is co-founder of th
International Interactive Computing Collaboration (2i2c)


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 and \mathbb. 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^3. Comm. Pure Appl. Math. 57 (2004), no. 8, 987–1014. *. *.


References


External links

* * * * {{DEFAULTSORT:Colliander, James 1967 births Living people Mathematical analysts Academic staff of the University of British Columbia Faculty of Science 20th-century American mathematicians 21st-century American mathematicians Canadian mathematicians University of Illinois Urbana-Champaign alumni