Jacob Lurie

Jacob Alexander Lurie (born December 7, 1977) is

an American mathematician who is a professor at the Jacob Lurie
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
Lurie in 2005
Montgomery Blair High School, Lurie took part in the
International Mathematical Olympiad, where he won a Born December 7, 1977
gold medal with a perfect score in 1994.[2] In 1996 he Washington, D.C., U.S.
took first place in the Westinghouse Science Talent Alma mater Harvard University (BA)
Search and was featured in a front-page story in the Massachusetts Institute of
Washington Times.[3] Technology (PhD)
Awards Morgan Prize (2000)
Lurie earned his bachelor's degree in mathematics from
Breakthrough Prize in
Harvard College in 2000 and was awarded in the same
Mathematics (2014)
year the Morgan Prize for his undergraduate thesis on
MacArthur Fellowship (2014)
Lie algebras.[4] He earned his Ph.D. from the
Massachusetts Institute of Technology under Scientific career
supervision of Michael J. Hopkins, in 2004 with a Fields Algebraic geometry
thesis on derived algebraic geometry. In 2007, he Institutions Massachusetts Institute of
became associate professor at MIT, and in 2009 he Technology
became professor at Harvard University.[5][6] In 2019, Harvard University
he joined the Institute for Advanced Study as a Institute for Advanced Study
permanent faculty member in mathematics.[7] Thesis Derived algebraic geometry (htt
ps://dspace.mit.edu/handle/172
1.1/30144) (2004)
Mathematical work Doctoral Michael J. Hopkins
advisor
Lurie's research interests started with logic and the
theory of surreal numbers when he was 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 (https://arxiv.org/abs/math.CT/060804
0), ISBN 978-0-691-14049-0, MR 2522659 (https://mathscinet.ams.org/mathscinet-getitem?
mr=2522659)
Lurie, Jacob (2017), Higher Algebra
Lurie, Jacob (2018), Spectral Algebraic Geometry

References
1. "Jacob Lurie" (https://www.ias.edu/scholars/lurie). Institute for Advanced Study. Retrieved
August 5, 2019.
2. Dillon, Sam (July 20, 1994), "Perfect Score for Americans in World Math Tourney" (https://w
ww.nytimes.com/1994/07/20/us/perfect-score-for-americans-in-world-math-tourney.html),
New York Times.
3. Lacharite, Gretchen (March 12, 1996), "Unreal mind gets top prize in science: Bethesda
teen wins talent search" (https://web.archive.org/web/20191212055453/https://www.questia.
com/read/1G1-56826719), Washington Times, archived from the original (https://www.questi
a.com/read/1G1-56826719) on December 12, 2019, retrieved January 7, 2019.
4. Lurie, Jacob (2001). "On simply laced Lie algebras and their minuscule representations" (htt
p://www.math.harvard.edu/~lurie/papers/thesis.pdf) (PDF). Commentarii Mathematici
Helvetici. 76 (3): 515–575. doi:10.1007/PL00013217 (https://doi.org/10.1007%2FPL000132
17). MR 1854697 (https://mathscinet.ams.org/mathscinet-getitem?mr=1854697).
S2CID 8543203 (https://api.semanticscholar.org/CorpusID:8543203).
5. "Jacob Lurie Named Professor of Mathematics at Harvard" (http://www.fas.harvard.edu/hom
e/news-and-notices/news/press-releases/release-archive/releases-2008/lurie-12182008.sht
ml), Harvard University, December 18, 2008.
6. Bradt, Steve (December 18, 2008). "Algebra, topology expert Lurie named professor of
mathematics" (http://news.harvard.edu/gazette/story/2008/12/algebra-topology-expert-lurie-
named-professor-of-mathematics/). Harvard Gazette. Retrieved June 24, 2014.
7. "Jacob Lurie, Trailblazing Mathematician, Joins Faculty of the Institute for Advanced Study"
(https://www.ias.edu/press-releases/2019/lurie-appointment). Institute for Advanced Study.
June 11, 2019. Retrieved August 5, 2019.
8. Conway, John H.; Jackson, Allyn (July 1996). "Budding Mathematician Wins Westinghouse
Competition" (https://www.ams.org/notices/199607/comm-conway.pdf) (PDF). Notices of the
American Mathematical Society. Retrieved September 26, 2016.
 9. "Five Winners Receive Inaugural Breakthrough Prize in Mathematics" (https://web.archive.or
g/web/20140624214039/https://breakthroughprize.org/?controller=Page&action=news&new
s_id=18). Breakthrough Prize. Archived from the original (https://breakthroughprize.org/?con
troller=Page&action=news&news_id=18) on June 24, 2014. Retrieved June 24, 2014.
10. "Jacob Lurie - MacArthur Fellow 2014" (http://www.macfound.org/fellows/921/). MacArthur
Foundation. Retrieved September 17, 2014.
11. Shay, Kevin James (September 29, 2014). "Blair alum wins prestigious MacArthur
fellowship" (https://web.archive.org/web/20180831035448/http://www.gazette.net/gazettecm
s/story.php?id=8508). Archived from the original (http://www.gazette.net/gazettecms/story.ph
p?id=8508) on August 31, 2018. Retrieved August 30, 2018.

External links
Lurie's website at the Institute for Advanced Study (https://www.ias.edu/scholars/lurie)
Lurie's website at Harvard (http://www.math.harvard.edu/~lurie/) (Jacob Lurie's Home Page
(http://math.ias.edu/~lurie/))
Jacob Lurie (https://mathgenealogy.org/id.php?id=84215) at the Mathematics Genealogy
Project
Jacob Lurie's results (https://www.imo-official.org/participant_r.aspx?id=1143) at
International Mathematical Olympiad

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