Jacob Lurie
Encyclopedia
Jacob Alexander Lurie is an American
mathematician
, who is currently a professor at Harvard University
.
, 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 Washington Times. He graduated from the Science, Mathematics, and Computer Science Magnet Program at Montgomery Blair High School
. 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 algebra
s. 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.
He is especially known for his work, starting with his thesis, on infinity-categories and derived algebraic geometry. Derived algebraic geometry is a way of infusion of homotopical
methods into algebraic geometry both to get deeper insight into algebraic geometry (e.g. into intersection theory
) and to use methods of algebraic geometry in stable homotopy theory. The latter is the topic of Lurie's work on elliptic cohomology
. Infinity categories (in the form of 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, which aroused much interest in the mathematical community, is his article on topological field theories
, where he sketches a classification of extended field theories using the language of infinity-categories.
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, who is currently a professor at Harvard University
Harvard University
Harvard University is a private Ivy League university located in Cambridge, Massachusetts, United States, established in 1636 by the Massachusetts legislature. Harvard is the oldest institution of higher learning in the United States and the first corporation chartered in the country...
.
Life
While in school, Lurie took part in the International Mathematical OlympiadInternational Mathematical Olympiad
The International Mathematical Olympiad is an annual six-problem, 42-point mathematical olympiad for pre-collegiate 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 in 1980...
, 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 Washington Times. He graduated from the Science, Mathematics, and Computer Science Magnet Program at Montgomery Blair High School
Montgomery Blair High School
Montgomery Blair High School is a public high school located in unincorporated Silver Spring in Montgomery County, Maryland, United States...
. Lurie earned his Bachelor's degree
Bachelor's degree
A bachelor's degree is usually an academic degree awarded for an undergraduate course or major that generally lasts for three or four years, but can range anywhere from two to six years depending on the region of the world...
in mathematics from Harvard College
Harvard College
Harvard College, in Cambridge, Massachusetts, is one of two schools within Harvard University granting undergraduate degrees...
in 2000 and was awarded in the same year the Morgan Prize
Morgan Prize
The Morgan Prize in Mathematics may refer to:* Frank and Brennie Morgan Prize for Outstanding Research in Mathematics by an Undergraduate Student awarded jointly by the American Mathematical Society, Mathematical Association of America and Society for Industrial and Applied Mathematics* De Morgan...
for his undergraduate thesis on Lie algebra
Lie algebra
In mathematics, a Lie algebra is an algebraic structure whose main use is in studying geometric objects such as Lie groups and differentiable manifolds. Lie algebras were introduced to study the concept of infinitesimal transformations. The term "Lie algebra" was introduced by Hermann Weyl in the...
s. He earned his Ph.D.
Doctor of Philosophy
Doctor of Philosophy, abbreviated as Ph.D., PhD, D.Phil., or DPhil , in English-speaking countries, is a postgraduate academic degree awarded by universities...
from the Massachusetts Institute of Technology
Massachusetts Institute of Technology
The Massachusetts Institute of Technology is a private research university located in Cambridge, Massachusetts. MIT has five schools and one college, containing a total of 32 academic departments, with a strong emphasis on scientific and technological education and research.Founded in 1861 in...
under supervision of Michael J. Hopkins
Michael J. Hopkins
Michael Jerome Hopkins is an American mathematician known for work in algebraic topology.-Life:He received his Ph.D. from Northwestern University in 1984 under the direction of Mark Mahowald. In 1984 he also received his D.Phil...
in 2004 with a thesis on derived algebraic geometry
Algebraic geometry
Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex...
. In 2007, he became associate professor at MIT, and in 2009 he became professor at Harvard.
Mathematical work
Lurie's research interests started with logic and the theory of surreal numbers, while he was still in school.He is especially known for his work, starting with his thesis, on infinity-categories and derived algebraic geometry. Derived algebraic geometry is a way of infusion of homotopical
Homotopy
In topology, two continuous functions from one topological space to another are called homotopic if one can be "continuously deformed" into the other, such a deformation being called a homotopy between the two functions...
methods into algebraic geometry both to get deeper insight into algebraic geometry (e.g. into intersection theory
Intersection theory
In mathematics, intersection theory is a branch of algebraic geometry, where subvarieties are intersected on an algebraic variety, and of algebraic topology, where intersections are computed within the cohomology ring. The theory for varieties is older, with roots in Bézout's theorem on curves and...
) and to use methods of algebraic geometry in stable homotopy theory. The latter is the topic of Lurie's work on elliptic cohomology
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 Joyal's
André Joyal
André Joyal is a professor of mathematics at the Université du Québec à Montréal who works on category theory. Joyal was born in Drummondville . He has three children and lives in Montreal.- Main research :...
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, which aroused much interest in the mathematical community, is his article on topological field theories
Topological quantum field theory
A topological quantum field theory is a quantum field theory which computes topological invariants....
, where he sketches a classification of extended field theories using the language of infinity-categories.