MacArthur Fellows Program

MacArthur Fellows / Meet the Class of 2014

Jacob Lurie

Mathematician

Professor, Department of Mathematics

Harvard University

Cambridge, Massachusetts

Age: 36 at time of award

Published September 17, 2014

Jacob Lurie is a mathematician creating a conceptual foundation for derived algebraic geometry (DAG). At an oversimplified level, he is transforming algebraic geometry to derived algebraic geometry—replacing the role of sets by topological spaces—making it applicable to other areas in new ways.

His ideas and methods are altering a range of fields, including higher category theory, topology, and geometry, while also influencing more distant fields such as representation theory and number theory. In two major treatises, Higher Topos Theory and Higher Algebra, along with subsequent papers comprising well over two thousand pages, Lurie redefines the foundations of homotopy theory and topological aspects of algebraic geometry, showing how many known concepts and results can be recast and improved in the framework of infinity-categories.  Lurie’s work is more than just a philosophical endeavor; he includes hard theorems in his foundations, developing theory to the point that deep new results become the corollary of a general and powerful framework. Illustrative of this is his proof of the cobordism hypothesis, a result that links purely categorical concepts of duality with the topology of manifolds and also supplies a classification of topological quantum field theories.

Lurie embraces an extraordinary breadth of vision—rewriting large swathes of mathematics from a new point of view—while also working to apply his foundational ideas to prove important new theorems in other areas. With an entire generation of young theorists currently being trained on Lurie’s new foundations, his greatest impact is yet to come.

Jacob Lurie received a B.S. (2000) from Harvard College and a Ph.D. (2004) from the Massachusetts Institute of Technology. He held a postdoctoral fellowship at Harvard University (2004­–2007) and was affiliated with the Massachusetts Institute of Technology (2007–2009) before joining the faculty of Harvard University, where he is currently a professor in the Department of Mathematics. His scientific work has been published in two books, Higher Topos Theory (2009) and Higher Algebra (2011), as well as numerous papers.

Photos

High-resolution photos for download. Photos are owned by the MacArthur Foundation and licensed under a Creative Commons license: CC-BY. Credit: John D. & Catherine T. MacArthur Foundation. Right-click on a link below to save the file to your computer.

For More Information

Website: www.math.harvard.edu/~lurie/

Jacob Lurie In the Media

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"A MacArthur for Math Professor"

Harvard Gazette
Jacob Lurie, 2014 MacArthur Fellow
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About the Fellows Program

The MacArthur Fellows Program awards unrestricted fellowships to talented individuals who have shown extraordinary originality and dedication in their creative pursuits and a marked capacity for self-direction. Learn More

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