mathematics

Victor Vasiliev

Victor Vasiliev 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 Victor Vasiliev rather than just read about it. In short: Victor Anatolyevich Vassiliev or Vasilyev (Russian: Виктор Анатольевич Васильев; born April 10, 1956), is a Soviet and Russian mathematician. He is best known for his discovery of the Vassiliev invariants in knot theory (also known as finite type invariants), which subsume many previously discovered polynomial knot invariants such as the Jones polynomial.

Key takeaways

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

Reference excerpt

Victor Anatolyevich Vassiliev or Vasilyev (Russian: Виктор Анатольевич Васильев; born April 10, 1956), is a Soviet and Russian mathematician. He is best known for his discovery of the Vassiliev invariants in knot theory (also known as finite type invariants), which subsume many previously discovered polynomial knot invariants such as the Jones polynomial. He also works on singularity theory, topology, computational complexity theory, integral geometry, symplectic geometry, partial differential equations (geometry of wavefronts), complex analysis, combinatorics, and Picard–Lefschetz theory.

Biography Vassiliev studied at the Faculty of Mathematics and Mechanics at the Lomonosov University in Moscow until 1981. From 1981 to 1987 he was Senior Researcher at the Documents and Archives Research Institute, Moscow and a part-time mathematics teacher at Specialized Mathematical School No. 57, Moscow. In 1982 he defended his Candidate of Sciences thesis under Vladimir Arnold and received the title of Doctor of Sciences in 1992. From 1987 to 1989 he was Senior Researcher at the Statistical Information Systems Research Institute in Moscow. From 1989 to 1990 he was Senior Researcher at the Department of Functional Analysis in the Keldysh Institute of Applied Mathematics in Moscow. From 1990 to 1995 he was Leading Researcher at the Department of Mathematics in the Research Institute for System Studies in Moscow. Since 1991 he has been professor at the Mathematics College of the Independent Moscow University. Since 1997 he has been Principal Researcher in the Department of Geometry and Topology at the Steklov Institute of Mathematics in Moscow. Since 2009 he has been professor and department chair in Higher School of Economics -Faculty of Mathematics, HSE. Since 2019 his is a member and first chairperson of the Russian Academy of Science's Commission against falsification of scientific research. He has been a visiting professor at the University of Paris VII, and at the Mathematical Sciences Research Institute (MSRI) at the University of California, Berkeley. He was a visiting fellow commoner at Trinity College, Cambridge in October–December 2000. Vasilyev has been a member of the Russian Academy of Science since 2003 (corresponding member since 1997). He is vice-chief editor of the Journal Functional Analysis and its Applications, and the president of the Moscow Mathematical Society. In 1994 he was an invited speaker at the International Mathematical Congress in Zürich (Plenary Address). In 1986 he received the Moscow Mathematical Society Award. On 21 February 2014 he together with other protesters against Bolotnaya Square case was arrested near Zamoskvoretsky Court in Moscow. On 5 March 2014 he among the other protesters was sentenced by Zamoskvoretsky Court to 10 thousand roubles (~ $150 US) fine for "resisting police". The European Parliament issued resolutions 2013/2667(RSP) of June 13, 2013 and resolution 2014/2628(RSP) of March 13, 2014 on the political nature of the Bolotnaya Square case. Prisoners of the case were recognized as prisoners of conscience by Amnesty International...Most of the people accused in the Bolotnaya square case then were amnestied in December 2013 due to the public pressure both at home and abroad in support of the political prisoners. Vassiliev is married, with three children. In 2022 he emigrated to Israel due to Russia's invasion of Ukraine.

References

Bar-Natan, Dror (1995), "On the Vassiliev knot invariants", Topology, 34 (2): 423–72, CiteSeerX 10.1.1.511.6301, doi:10.1016/0040-9383(95)93237-2 {{citation}}: Cite uses deprecated parameter |citeseerx= (help) Kontsevich, Maxim (1993), "Vassiliev's knot invariants", I. M. Gelfand Seminar, Part 2, ADVSOV, vol. 16, pp. 137–50, doi:10.1090/advsov/016.2/04, ISBN 9780821841174

External links Vassiliev Invariant, Math World. Vassiliev, The Steklov Institute.

Illustrations

Worked examples

Example 1 — a first encounter with Victor Vasiliev

Start with the simplest possible case. Write down what Victor Vasiliev 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 Victor Vasiliev 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 Victor Vasiliev 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 Victor Vasiliev

In research: Victor Vasiliev 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 Victor Vasiliev 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: Victor Vasiliev is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1956 births, 20th-century Russian mathematicians, 21st-century Russian mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Victor Vasiliev 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 Victor Vasiliev in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Victor Vasiliev 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 Victor Vasiliev out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Victor Vasiliev in simple terms?

Why does Victor Vasiliev 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 Victor Vasiliev?

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 Victor Vasiliev.