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 schola ...

. 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, excep ...

, 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 si ...

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 ...

in 2000 and was awarded in the same year the Morgan Prize for his undergraduate thesis on

Lie algebra In mathematics, a Lie algebra (pronounced ) is a vector space \mathfrak g together with an operation called the Lie bracket, an alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow \mathfrak g, that satisfies the Jacobi identi ...

s. He earned his Ph.D. 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 th ...

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 Decompositi ...

, 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 commutativ ...

. In 2007, he became associate professor at MIT, 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 highe ...

. 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 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 In mathematics, stable homotopy theory is the part of homotopy theory (and thus algebraic topology) concerned with all structure and phenomena that remain after sufficiently many applications of the suspension functor. A founding result was the F ...

. 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 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 an algebraic-geometric setting, to prove the

Siegel mass formula Siegel (also Segal or Segel), is a German and Ashkenazi Jewish surname. it can be traced to 11th century Bavaria and was used by people who made wax seals for or sealed official documents (each such male being described as a ''Siegelbeamter''). A ...

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 Pri ...

in 2014, "for his work on the foundations of higher category theory 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