Jacob Alexander Lurie (born December 7, 1977) is an American

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, structure, space, models, and change. History On ...

who is a professor at the

Institute for Advanced Study The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholar ...

. Lurie is a 2014 MacArthur Fellow.

Life

When he was a student in the Science, Mathematics, and Computer Science Magnet Program at

Montgomery Blair High School Montgomery Blair High School (MBHS) is a public high school located in Four Corners, Maryland, United States, operated by Montgomery County Public Schools. The school's total enrollment of 3,600 makes it the largest public high school in Montgo ...

, Lurie took part in the

International Mathematical Olympiad The International Mathematical Olympiad (IMO) is a mathematical olympiad for pre-university students, and is the oldest of the International Science Olympiads. The first IMO was held in Romania in 1959. It has since been held annually, except i ...

, where he won a gold medal with a perfect score in 1994. In 1996 he took first place in the

Westinghouse Science Talent Search Westinghouse may refer to: Businesses Current companies *Westinghouse Electric Corporation, the company that manages the Westinghouse brand, with licensees: **Westinghouse Electric Company, providing nuclear power-related services ** Westingho ...

and was featured in a front-page story in the ''

Washington Times ''The Washington Times'' is an American conservative daily newspaper published in Washington, D.C., that covers general interest topics with a particular emphasis on national politics. Its broadsheet daily edition is distributed throughout ...

''. Lurie earned his

bachelor's degree A bachelor's degree (from Middle Latin ''baccalaureus'') or baccalaureate (from Modern Latin ''baccalaureatus'') is an undergraduate academic degree awarded by colleges and universities upon completion of a course of study lasting three to six ...

in mathematics from

Harvard College Harvard College is the undergraduate college of Harvard University, an Ivy League research university in Cambridge, Massachusetts. Founded in 1636, Harvard College is the original school of Harvard University, the oldest institution of higher lea ...

in 2000 and was awarded in the same year the

Morgan Prize :''Distinguish from the De Morgan Medal awarded by the London Mathematical Society.'' The Morgan Prize (full name Frank and Brennie Morgan Prize for Outstanding Research in Mathematics by an Undergraduate Student) is an annual award given to an un ...

for his undergraduate thesis on Lie algebras. He earned his

Ph.D. A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is ...

from the

Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the ...

under supervision of

Michael J. Hopkins Michael Jerome Hopkins (born April 18, 1958) is an American mathematician known for work in algebraic topology. Life He received his PhD from Northwestern University in 1984 under the direction of Mark Mahowald, with thesis ''Stable Decompositio ...

, in 2004 with a thesis on

derived algebraic geometry Derived algebraic geometry is a branch of mathematics that generalizes algebraic geometry to a situation where commutative rings, which provide local charts, are replaced by either differential graded algebras (over \mathbb), simplicial commutati ...

. In 2007, he became associate professor at

MIT The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the m ...

, and in 2009 he became professor at

Harvard University Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher le ...

. In 2019, he joined the

as a permanent faculty member in mathematics.

Mathematical work

Lurie's research interests started with logic and the theory of

surreal numbers In mathematics, the surreal number system is a totally ordered proper class containing the real numbers as well as infinite and infinitesimal numbers, respectively larger or smaller in absolute value than any positive real number. The surrea ...

while he was still in high school. He is best known for his work, starting with his thesis, on infinity categories and

. 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 In mathematics, intersection theory is one of the main branches of algebraic geometry, where it gives information about the intersection of two subvarieties of a given variety. The theory for varieties is older, with roots in Bézout's theorem o ...

) 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 In mathematics, elliptic cohomology is a cohomology theory in the sense of algebraic topology. It is related to elliptic curves and modular forms. History and motivation Historically, elliptic cohomology arose from the study of elliptic genera. ...

. Infinity categories (in the form of

André Joyal André Joyal (; born 1943) is a professor of mathematics at the Université du Québec à Montréal who works on category theory. He was a member of the School of Mathematics at the Institute for Advanced Study in 2013, where he was invited to jo ...

'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 mathematics, the cobordism hypothesis, due to John C. Baez and James Dolan, concerns the classification of extended topological quantum field theories (TQFTs). In 2008, Jacob Lurie outlined a proof of the cobordism hypothesis, though the deta ...

). In joint work with

Dennis Gaitsgory Dennis Gaitsgory is a professor of mathematics at Harvard University known for his research on the geometric Langlands program. Born in Chișinău, now in Moldova, he grew up in Tajikistan, before studying at Tel Aviv University under Joseph Be ...

, he used his non-abelian

Poincaré duality In mathematics, the Poincaré duality theorem, named after Henri Poincaré, is a basic result on the structure of the homology and cohomology groups of manifolds. It states that if ''M'' is an ''n''-dimensional oriented closed manifold (compact ...

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 The Breakthrough Prize in Mathematics is an annual award of the Breakthrough Prize series announced in 2013. It is funded by Yuri Milner and Mark Zuckerberg and others. The annual award comes with a cash gift of $3 million. The Breakthrough Prize ...

in 2014, "for his work on the foundations of

higher category theory In mathematics, higher category theory is the part of category theory at a ''higher order'', which means that some equalities are replaced by explicit arrows in order to be able to explicitly study the structure behind those equalities. Higher cate ...

and

; for the classification of fully extended topological quantum field theories; and for providing a moduli-theoretic interpretation of elliptic cohomology." Lurie was also awarded a MacArthur "Genius Grant" Fellowship in 2014.

Publications

References

External links

Lurie's website at the Institute for Advanced StudyLurie's website at HarvardJacob Lurie's Home Page
* * {{DEFAULTSORT:Lurie, Jacob 1977 births Living people People from Washington, D.C. 21st-century American mathematicians Harvard College alumni MacArthur Fellows Massachusetts Institute of Technology alumni Harvard University faculty International Mathematical Olympiad participants Category theorists Higher category theory Institute for Advanced Study faculty