Vyacheslav Shokurov proved the scheme analog of the Noether–Enriques–Petri theorem in 1970 while still an undergraduate at the Lomonosov Moscow State University. This early success laid the groundwork for his extensive contributions to algebraic geometry, specifically in birational geometry and the Minimal Model Program, where he has redefined understanding of three-dimensional and four-dimensional varieties.
Academic Beginnings
Born in Moscow in 1950, Shokurov entered the Faculty of Mechanics and Mathematics at Moscow State University in 1968. Under the supervision of Yuri Manin, he focused his doctoral studies on the geometry of Kuga varieties. He earned his Ph.D. in 1976, following early research that addressed Schottky-type problems and the existence of lines on smooth Fano varieties.
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During his tenure at Yaroslavl State Pedagogical University, Shokurov worked alongside Vasily Iskovskikh and Zalman Skopec. He solved critical problems regarding the rationality of standard conic bundles and established criteria for Prym varieties. His 1983 paper, Prym varieties: theory and applications, concluded significant research into the relationship between polarized Prym varieties and the Jacobians of smooth curves.
Minimal Model Program
In the mid-1980s, Shokurov shifted his attention toward the Minimal Model Program. His 1985 paper on nonvanishing theorems provided a foundational pillar for the cone and semi-ampleness theorems. He achieved the termination of three-dimensional flips and later announced the existence of four-dimensional log flips in 2001, findings detailed in his texts on birational geometry and finitely-generated algebras.
Current Professional Engagements
Shokurov serves as a professor at Johns Hopkins University in Baltimore while maintaining an association with the Steklov Institute of Mathematics in Moscow. His teaching career includes the supervision of nine doctoral students, among them Caucher Birkar, Florin Ambro, Ivan Cheltsov, Jihun Park, Sung Rak Choi, Yifei Chen, Joseph Cutrone, and Nicholas Marshburn.
Fast facts
- Born: 1950, Moscow
- Citizenship: Russia
- Education: MSU Faculty of Mechanics and Mathematics
- Doctoral Advisor: Yuri Manin
- Primary Field: Algebraic geometry
- Current Employer: Johns Hopkins University
- Ph.D. Year: 1976
Questions readers ask
What is Shokurov best known for?
He is recognized for his research in algebraic geometry, specifically his proof of the cone theorem and the existence of log flips.
Where does Vyacheslav Shokurov teach?
He is a professor at Johns Hopkins University and a faculty member at the Steklov Institute of Mathematics.
Achievements
- Held posts at Johns Hopkins University and Steklov Institute of Mathematics
- Fields: algebraic geometry and algebra
