The development of a patchworking technique in algebraic geometry enabled Oleg Viro to construct real algebraic varieties through a cut and paste methodology. This mathematical advancement provided a foundation for the evolution of tropical geometry, while his joint research with Vladimir Turaev established invariants within the domain of topological quantum field theory.
Academic Foundations and Early Career
Born in 1948 in Saint Petersburg, Viro pursued his education at the Mathematics and Mechanics Faculty of Saint Petersburg State University. He earned his Doctor of Sciences in Physics and Mathematics, completing his PhD studies in 1974 under the supervision of Vladimir Rokhlin. Following his academic training, he held a teaching position at Leningrad State University from 1973 until 1991.
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Viro's work focuses on the intersection of topology, knot theory, and algebraic geometry. His patchworking method facilitated the isotopy classification of non-singular plane projective curves of degree 7. Furthermore, the Turaev-Viro invariants created in collaboration with Vladimir Turaev linked topological quantum field theory with established geometric principles, marking a significant contribution to the field.
Professional Appointments and Institutional Roles
Throughout his career, Viro held faculty positions at several international institutions. He served as the F. B. Jones chair professor in Topology at the University of California, Riverside, between 1992 and 1997. Additionally, he held a professorship at Uppsala University in Sweden from 1994 to 2003. He maintained long-term ties to the Saint Petersburg Department of the Steklov Institute of Mathematics and currently serves as a professor at Stony Brook University.
Professional Recognition
Viro served as an invited speaker at the 1983 International Congress of Mathematicians in Warsaw and the 2000 European Congress of Mathematicians in Barcelona. The Swedish government awarded him the Göran Gustafsson Prize in 1997. In 2013, he was recognized as a Fellow of the American Mathematical Society, reflecting his standing within the global mathematical community.
Fast facts
- Born: 1948, Saint Petersburg
- Citizenship: United States, Soviet Union
- Academic Degree: Doctor of Sciences in Physics and Mathematics
- Field of Study: Algebraic geometry, topology, knot theory
- Primary Professional Focus: Patchworking technique
- Fellowship: American Mathematical Society (2013)
- Languages: English, Russian
Questions readers ask
What is the patchworking technique?
It is an algebraic geometry method developed by Viro to construct real algebraic varieties by cutting and pasting.
What are Turaev-Viro invariants?
These are topological invariants developed jointly by Oleg Viro and Vladimir Turaev, connected to topological quantum field theory.
Achievements
- Held posts at University of California, Riverside, Uppsala University and Stony Brook University
- Fields: algebraic geometry, topology and mathematics
