mathematics

Oleg Viro

Oleg Viro is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Oleg Viro rather than just read about it. In short: Oleg Yanovich Viro (Russian: Олег Янович Виро) (b. 13 May 1948, Leningrad, USSR) is a Russian mathematician in the fields of topology and algebraic geometry, most notably real algebraic geometry, tropical geometry and knot theory. Contributions Viro developed a "patchworking" technique in algebraic geometry, which allows real algebraic varieties to be constructed by a "cut and paste" method.

Key takeaways

Oleg Viro belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Oleg Viro to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Oleg Viro from memory before moving on to harder problems.

Reference excerpt

Oleg Yanovich Viro (Russian: Олег Янович Виро) (b. 13 May 1948, Leningrad, USSR) is a Russian mathematician in the fields of topology and algebraic geometry, most notably real algebraic geometry, tropical geometry and knot theory.

Contributions

Viro developed a "patchworking" technique in algebraic geometry, which allows real algebraic varieties to be constructed by a "cut and paste" method. Using this technique, Viro completed the isotopy classification of non-singular plane projective curves of degree 7. The patchworking technique was one of the fundamental ideas which motivated the development of tropical geometry. In topology, Viro is most known for his joint work with Vladimir Turaev, in which the Turaev–Viro invariants (relatives of the Reshetikhin-Turaev invariants) and related topological quantum field theory notions were introduced.

Education and career Viro studied at the Leningrad State University where he received his Ph.D. degree in 1974; his advisor was Vladimir Rokhlin. Viro taught from 1973 until 1991 at Leningrad State University. Since 1986 he has been a member of the Saint Petersburg Department of the Steklov Institute of Mathematics. In 1992-1997, Viro was a F. B. Jones chair professor in Topology at the University of California, Riverside. In 1994-2003 he was a professor at Uppsala University, Sweden. On 8 February 2007, Viro and his colleague Burglind Juhl-Jöricke were forced to resign from the university. There had been a history of conflict at the Mathematics Institute, with allegations of disagreeable behavior by several parties in the conflict. A number of Swedish, European and American mathematicians protested the manner in which the two Professors of Mathematics were forced to resign. These protests include the following:

an open letter by Lennart Carleson, former president of the International Mathematical Union, a letter by Ari Laptev, current president of the European Mathematical Society, and a letter from M. Salah Baouendi, Arthur Jaffe, Joel Lebowitz, Elliott H. Lieb and Nicolai Reshetikhin. As of 2009, Viro is a senior researcher at the St. Petersburg Department of the Steklov Institute of Mathematics, and a professor at Stony Brook University.

Awards and honors Viro was an invited speaker at the International Congress of Mathematicians in 1983 (Warsaw) and the European Congress of Mathematicians in 2000 (Barcelona). He was awarded the Göran Gustafsson Prize (1997) by the Swedish government. In 2012 he became a fellow of the American Mathematical Society.

References

External links Oleg Viro's website

Illustrations

Oleg Viro: Oleg Viro in 2008 at the Mathematical Research Institute of Oberwolfach — Oleg Viro in 2008 at the Mathematical Research Institute of Oberwolfach

Worked examples

Example 1 — a first encounter with Oleg Viro

Start with the simplest possible case. Write down what Oleg Viro claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Oleg Viro before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Oleg Viro ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Oleg Viro

In research: Oleg Viro appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Oleg Viro in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Oleg Viro is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1948 births, 20th-century Russian mathematicians, 21st-century Russian mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Oleg Viro outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Oleg Viro in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Oleg Viro means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Oleg Viro out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Oleg Viro in simple terms?

Why does Oleg Viro matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Oleg Viro?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Oleg Viro.