Ravi Vakil
Encyclopedia
Ravi D. Vakil is an American-Canadian mathematician working in algebraic geometry
.
Vakil attended high school at Martingrove Collegiate Institute
in Etobicoke, Ontario
, where he won several mathematical contests and olympiads. After earning a BSc and MSc from the University of Toronto
in 1992, he completed a Ph.D. in mathematics at Harvard University
in 1997 under Joe Harris
. He has since been an instructor at both Princeton University
and MIT
. Since the fall of 2001, he has taught at Stanford University
, becoming a full professor in 2007.
Vakil is an algebraic geometer
and his research work spans over enumerative geometry
, topology
, Gromov–Witten theory, and classical algebraic geometry. He has solved several old problems in Schubert calculus
. Among other results, he proved that all Schubert problems are enumerative over the real number
s, a result that resolves an issue mathematicians have worked on for at least two decades.
Vakil has received many awards, including an NSF
Career Fellowship, a Sloan
Research Fellowship, an American Mathematical Society
Centennial Fellowship, a G. de B. Robinson Prize for the best paper published in the Canadian Journal of Mathematics and the Canadian Mathematical Bulletin
, and the André-Aisenstadt Prize from the Centre de Recherches Mathématiques
at the Université de Montréal
.
He has participated with the Canadian team in three IMO
's winning two gold and one silver medals and was 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.
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...
.
Vakil attended high school at Martingrove Collegiate Institute
Martingrove Collegiate Institute
Martingrove Collegiate Institute is a non-semestered public secondary school located on the southeast corner at the intersection of Eglinton Avenue and Martin Grove Road in Toronto, Ontario, Canada. It is overseen by the Toronto District School Board. The school is home to the gifted program in...
in Etobicoke, Ontario
Ontario
Ontario is a province of Canada, located in east-central Canada. It is Canada's most populous province and second largest in total area. It is home to the nation's most populous city, Toronto, and the nation's capital, Ottawa....
, where he won several mathematical contests and olympiads. After earning a BSc and MSc from the University of Toronto
University of Toronto
The University of Toronto is a public research university in Toronto, Ontario, Canada, situated on the grounds that surround Queen's Park. It was founded by royal charter in 1827 as King's College, the first institution of higher learning in Upper Canada...
in 1992, he completed a Ph.D. in mathematics 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...
in 1997 under Joe Harris
Joseph Daniel Harris
Joseph Daniel Harris , known nearly universally as Joe Harris, is a mathematician at Harvard University working in the field of algebraic geometry. He attended college at and received his Ph.D. from Harvard in 1978 under Phillip Griffiths....
. He has since been an instructor at both Princeton University
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
and MIT
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...
. Since the fall of 2001, he has taught at Stanford University
Stanford University
The Leland Stanford Junior University, commonly referred to as Stanford University or Stanford, is a private research university on an campus located near Palo Alto, California. It is situated in the northwestern Santa Clara Valley on the San Francisco Peninsula, approximately northwest of San...
, becoming a full professor in 2007.
Vakil is an algebraic geometer
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...
and his research work spans over enumerative geometry
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:...
, topology
Topology
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...
, Gromov–Witten theory, and classical algebraic geometry. He has solved several old problems in Schubert calculus
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...
. Among other results, he proved that all Schubert problems are enumerative over the real number
Real number
In mathematics, a real number is a value that represents a quantity along a continuum, such as -5 , 4/3 , 8.6 , √2 and π...
s, a result that resolves an issue mathematicians have worked on for at least two decades.
Vakil has received many awards, including an NSF
National Science Foundation
The National Science Foundation is a United States government agency that supports fundamental research and education in all the non-medical fields of science and engineering. Its medical counterpart is the National Institutes of Health...
Career Fellowship, a Sloan
Alfred P. Sloan Foundation
The Alfred P. Sloan Foundation is a philanthropic non-profit organization in the United States. It was established in 1934 by Alfred P. Sloan, Jr., then-President and Chief Executive Officer of General Motors.-Overview:...
Research Fellowship, an American Mathematical Society
American Mathematical Society
The American Mathematical Society is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, which it does with various publications and conferences as well as annual monetary awards and prizes to mathematicians.The society is one of the...
Centennial Fellowship, a G. de B. Robinson Prize for the best paper published in the Canadian Journal of Mathematics and the Canadian Mathematical Bulletin
Canadian Mathematical Society
The Canadian Mathematical Society is an association of professional mathematicians dedicated to the interests of mathematical research and education in Canada.It was originally conceived in June 1945 as the Canadian Mathematical Congress...
, and the André-Aisenstadt Prize from the Centre de Recherches Mathématiques
Centre de Recherches Mathématiques
The Centre de Recherches Mathématiques is the first mathematical research institute in Canada. It was founded in 1969, and was recognized as a national research center for the mathematical sciences in 1984....
at the Université de Montréal
Université de Montréal
The Université de Montréal is a public francophone research university in Montreal, Quebec, Canada. It comprises thirteen faculties, more than sixty departments and two affiliated schools: the École Polytechnique and HEC Montréal...
.
He has participated with the Canadian team in three IMO
IMO
The three-letter acronym IMO may refer to:* International Mathematical Olympiad* International Maritime Organization** IMO ship identification number, unique identity numbers issued to seacraft * International Meteorological Organization...
's winning two gold and one silver medals and was the fourth person to be a four-time Putnam
William Lowell Putnam Mathematical Competition
The William Lowell Putnam Mathematical Competition, often abbreviated to the Putnam Competition, is an annual mathematics competition for undergraduate college students of the United States and Canada, awarding scholarships and cash prizes ranging from $250 to $2,500 for the top students and $5,000...
Fellow in the history of the contest. Also, he has been the coordinator of weekly Putnam preparation seminars at Stanford.