Jacob Alexander Lurie (born December 7, 1977) is an American mathematician who is a professor at the

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

. In 2014, Lurie received a

MacArthur Fellowship The MacArthur Fellows Program, also known as the MacArthur Fellowship and colloquially called the "Genius Grant", is a prize awarded annually by the MacArthur Foundation, John D. and Catherine T. MacArthur Foundation to typically between 20 and ...

. Lurie's research interests are

algebraic geometry Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometry, geometrical problems. Classically, it studies zero of a function, zeros of multivariate polynomials; th ...

topology Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformat ...

, and

homotopy theory In mathematics, homotopy theory is a systematic study of situations in which Map (mathematics), maps can come with homotopy, homotopies between them. It originated as a topic in algebraic topology, but nowadays is learned as an independent discipli ...

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 The International Mathematical Olympiad (IMO) is a mathematical olympiad for pre-university students, and is the oldest of the International Science Olympiads. It is widely regarded as the most prestigious mathematical competition in the wor ...

, where he won a gold medal with a perfect score in 1994. In 1996 he took first place in the Westinghouse Science Talent Search and was featured in a front-page story in the '' Washington Times''. Lurie earned his

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

in mathematics from

Harvard College Harvard College is the undergraduate education, undergraduate college of Harvard University, a Private university, private Ivy League research university in Cambridge, Massachusetts, United States. Part of the Harvard Faculty of Arts and Scienc ...

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 ident ...

s. He earned his Ph.D. from the

Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a Private university, private research university in Cambridge, Massachusetts, United States. Established in 1861, MIT has played a significant role in the development of many areas of moder ...

under supervision of Michael J. Hopkins, 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 commutative ...

. In 2007, he became associate professor at

MIT The Massachusetts Institute of Technology (MIT) is a private research university in Cambridge, Massachusetts, United States. Established in 1861, MIT has played a significant role in the development of many areas of modern technology and sc ...

, and in 2009 he became professor at

Harvard University Harvard University is a Private university, private Ivy League research university in Cambridge, Massachusetts, United States. Founded in 1636 and named for its first benefactor, the History of the Puritans in North America, Puritan clergyma ...

. In 2019, he joined the

as a permanent faculty member in mathematics. Lurie is

Jewish Jews (, , ), or the Jewish people, are an ethnoreligious group and nation, originating from the Israelites of History of ancient Israel and Judah, ancient Israel and Judah. They also traditionally adhere to Judaism. Jewish ethnicity, rel ...

Mathematical work

Lurie's research interests started with

logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure o ...

and the theory of

surreal number In mathematics, the surreal number system is a total order, totally ordered proper class containing not only the real numbers but also Infinity, infinite and infinitesimal, infinitesimal numbers, respectively larger or smaller in absolute value th ...

s when he was 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

, 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. 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 mathematics, the Poincaré duality theorem, named after Henri Poincaré, is a basic result on the structure of the homology (mathematics), homology and cohomology group (mathematics), groups of manifolds. It states that if ''M'' is an ''n''-dim ...

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

and derived algebraic geometry; 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

* *Lurie, Jacob (2017), ''Higher Algebra'' *Lurie, Jacob (2018), ''Spectral Algebraic Geometry''

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 Department of Mathematics faculty International Mathematical Olympiad participants Category theorists Higher category theory Institute for Advanced Study faculty