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American mathematician
Jacob Alexander Lurie (born December 7, 1977) is an American mathematician who is a professor at the
Institute for Advanced Study .
[1] In 2014, Lurie received a
MacArthur Fellowship .
Life
When he was a student in the Science, Mathematics, and Computer Science Magnet Program at
Montgomery Blair High School , Lurie took part in the
International Mathematical Olympiad , where he won a gold medal with a perfect score in 1994.
[2] In 1996 he took first place in the
Westinghouse Science Talent Search and was featured in a front-page story in the
Washington Times .
[3]
Lurie earned his
bachelor's degree in mathematics from
Harvard College in 2000 and was awarded in the same year the
Morgan Prize for his undergraduate thesis on
Lie algebras .
[4] He earned his
Ph.D. from the
Massachusetts Institute of Technology under supervision of
Michael J. Hopkins , in 2004 with a thesis on
derived algebraic geometry . In 2007, he became associate professor at
MIT , and in 2009 he became professor at
Harvard University .
[5]
[6] In 2019, he joined the
Institute for Advanced Study as a permanent faculty member in mathematics.
[7]
Mathematical work
Lurie's research interests started with logic and the theory of
surreal numbers while he was still in high school.
[8] He is best known for his work, starting with his thesis, on
infinity categories and
derived algebraic geometry . Derived algebraic geometry is a way of infusing
homotopical methods into algebraic geometry, with two purposes: deeper insight into algebraic geometry (e.g. into
intersection theory ) and the use of methods of algebraic geometry in
stable homotopy theory . The latter area is the topic of Lurie's work on
elliptic cohomology .
Infinity categories (in the form of
André Joyal 's quasi-categories) are a convenient framework to do homotopy theory in abstract settings. They are the main topic of his book Higher Topos Theory .
Another part of Lurie's work is his article on
topological field theories , where he sketches a classification of extended field theories using the language of infinity categories (
cobordism hypothesis ). In joint work with
Dennis Gaitsgory , he used his non-abelian
Poincaré duality in an algebraic-geometric setting, to prove the
Siegel mass formula for
function fields .
Lurie was one of the inaugural winners of the
Breakthrough Prize in Mathematics in 2014, "for his work on the foundations of
higher category theory and
derived algebraic geometry ; for the classification of fully extended topological quantum field theories; and for providing a moduli-theoretic interpretation of elliptic cohomology."
[9] Lurie was also awarded a MacArthur "genius grant" Fellowship in 2014.
[10]
[11]
Publications
Lurie, Jacob (2009),
Higher Topos Theory , Annals of Mathematics Studies, vol. 170,
Princeton University Press ,
arXiv :
math.CT/0608040 ,
ISBN
978-0-691-14049-0 ,
MR
2522659
Lurie, Jacob (2017), Higher Algebra
Lurie, Jacob (2018), Spectral Algebraic Geometry
References
^
"Jacob Lurie" . Institute for Advanced Study . Retrieved August 5, 2019 .
^ Dillon, Sam (July 20, 1994),
"Perfect Score for Americans in World Math Tourney" ,
New York Times .
^ Lacharite, Gretchen (March 12, 1996),
"Unreal mind gets top prize in science: Bethesda teen wins talent search" ,
Washington Times .
^ Lurie, Jacob (2001).
"On simply laced Lie algebras and their minuscule representations" (PDF) .
Commentarii Mathematici Helvetici . 76 (3): 515–575.
doi :
10.1007/PL00013217 .
MR
1854697 .
S2CID
8543203 .
^
"Jacob Lurie Named Professor of Mathematics at Harvard" , Harvard University , December 18, 2008 .
^ Bradt, Steve (December 18, 2008).
"Algebra, topology expert Lurie named professor of mathematics" . Harvard Gazette. Retrieved June 24, 2014 .
^
"Jacob Lurie, Trailblazing Mathematician, Joins Faculty of the Institute for Advanced Study" . Institute for Advanced Study . Retrieved August 5, 2019 .
^ Conway, John H.; Jackson, Allyn (July 1996).
"Budding Mathematician Wins Westinghouse Competition" (PDF) . Notices of the American Mathematical Society. Retrieved September 26, 2016 .
^
"Five Winners Receive Inaugural Breakthrough Prize in Mathematics" . Breakthrough Prize . Archived from
the original on June 24, 2014. Retrieved June 24, 2014 .
^
"Jacob Lurie - MacArthur Fellow 2014" . MacArthur Foundation. Retrieved September 17, 2014 .
^ Shay, Kevin James (September 29, 2014).
"Blair alum wins prestigious MacArthur fellowship" . Retrieved August 30, 2018 .
External links
Mathematics
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