Ravi D. Vakil (born February 22, 1970) is a Canadian-American mathematician working in

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 ...

. He is the current president of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

Education and career

Vakil attended high school at

Martingrove Collegiate Institute Martingrove Collegiate Institute is a semestered public secondary school in the Etobicoke district of Toronto, Ontario, Canada. It opened in 1966 and is currently overseen by the Toronto District School Board. Academics Gifted Program Marting ...

Etobicoke Etobicoke (, ) is an administrative district and former city within Toronto, Ontario, Canada. Comprising the city's west end, Etobicoke is bordered on the south by Lake Ontario, on the east by the Humber River (Ontario), Humber River, on the ...

, Ontario, where he won several mathematical contests and olympiads. After earning a BSc and MSc from the

University of Toronto The University of Toronto (UToronto or U of T) is a public university, public research university whose main campus is located on the grounds that surround Queen's Park (Toronto), Queen's Park in Toronto, Ontario, Canada. It was founded by ...

in 1992, he completed a PhD in mathematics 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 1997 under Joe Harris. He has since been an instructor at both

Princeton University Princeton University is a private university, private Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial ...

and

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 ...

. Since the fall of 2001, he has taught at

Stanford University Leland Stanford Junior University, commonly referred to as Stanford University, is a Private university, private research university in Stanford, California, United States. It was founded in 1885 by railroad magnate Leland Stanford (the eighth ...

, becoming a full professor in 2007. '' The Rising Sea: Foundations of Algebraic Geometry'', a mathematical textbook about algebraic geometry by Ravi Vakil, will be published in 2025, although drafts have already been available online ever since he began to write in 2010.

Contributions

Vakil is an algebraic geometer and his research work spans over

enumerative geometry In mathematics, enumerative geometry is the branch of algebraic geometry concerned with counting numbers of solutions to geometric questions, mainly by means of intersection theory. History The problem of Apollonius is one of the earliest exam ...

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 ...

, Gromov–Witten theory, and classical algebraic geometry. He has solved several old problems in

Schubert calculus In mathematics, Schubert calculus is a branch of algebraic geometry introduced in the nineteenth century by Hermann Schubert in order to solve various counting problems of projective geometry and, as such, is viewed as part of enumerative geometr ...

. Among other results, he proved that all Schubert problems are enumerative over the

real number In mathematics, a real number is a number that can be used to measure a continuous one- dimensional quantity such as a duration or temperature. Here, ''continuous'' means that pairs of values can have arbitrarily small differences. Every re ...

s, a result that resolves an issue mathematicians have worked on for at least two decades.

Awards and honors

Vakil has received many awards, including an

NSF NSF may stand for: Political organizations *National Socialist Front, a Swedish National Socialist party *NS-Frauenschaft, the women's wing of the former German Nazi party * National Students Federation, a leftist Pakistani students' political g ...

CAREER Fellowship, a Sloan Research Fellowship, an

Centennial Fellowship, a G. de B. Robinson prize for the best paper published (2000) in the

Canadian Journal of Mathematics The ''Canadian Journal of Mathematics'' () is a bimonthly mathematics journal published by the Canadian Mathematical Society. It was established in 1949 by H. S. M. Coxeter and G. de B. Robinson. The current editors-in-chief of the journal ar ...

and the

Canadian Mathematical Bulletin The ''Canadian Mathematical Bulletin'' () is a mathematics journal, established in 1958 and published quarterly by the Canadian Mathematical Society. The current editors-in-chief of the journal are Antonio Lei and Javad Mashreghi. The journal p ...

, and the André-Aisenstadt Prize from the

Centre de Recherches Mathématiques The Centre de recherches mathématiques (CRM) is the first mathematical research institute in Canada, located at the Université de Montréal. The CRM has ten research laboratories, one in each of: mathematical analysis, number theory and symbolic ...

at the

Université de Montréal The Université de Montréal (; UdeM; ) is a French-language public research university in Montreal, Quebec, Canada. The university's main campus is located in the Côte-des-Neiges neighborhood of Côte-des-Neiges–Notre-Dame-de-Grâce on M ...

(2005), and the

Chauvenet Prize The Chauvenet Prize is an annual award given by the Mathematical Association of America in recognition of an outstanding expository article on a mathematical topic. It consists of a prize of $1,000 and a certificate. The Chauvenet Prize was the ...

(2014). In 2013 he became a fellow of the

. Vakil was elected as its president in 2024 and began his two-year term on 1 February 2025.

Mathematics contests

He was a member of the Canadian team in three

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 ...

s, winning silver, gold (perfect score), and gold in 1986, 1987, and 1988 respectively. He was also the fourth person to be a four-time Putnam Fellow in the history of the contest. Also, he has been the coordinator of weekly Putnam preparation seminars at Stanford.

References

External links

Ravi Vakil's Home Page
* *
The Rising Sea , Ravi's notes on algebraic geometry
{{DEFAULTSORT:Vakil, Ravi 1970 births University of Toronto alumni Harvard Graduate School of Arts and Sciences alumni Stanford University faculty Algebraic geometers 20th-century American mathematicians 21st-century American mathematicians Canadian mathematicians People from Etobicoke Putnam Fellows Living people Canadian people of Indian descent Fellows of the American Mathematical Society International Mathematical Olympiad participants Recipients of the Presidential Early Career Award for Scientists and Engineers