mathematics

Nicolai Reshetikhin

Nicolai Reshetikhin 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 Nicolai Reshetikhin rather than just read about it. In short: Nicolai Yuryevich Reshetikhin (Russian: Николай Юрьевич Решетихин, born October 10, 1958, in Leningrad, Soviet Union) is a mathematical physicist, currently a professor of mathematics at Tsinghua University, China and a professor of mathematical physics at the University of Amsterdam (Korteweg-de Vries Institute for Mathematics). He is also a professor emeritus at the University of California, Berkeley.

Key takeaways

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

Reference excerpt

Nicolai Yuryevich Reshetikhin (Russian: Николай Юрьевич Решетихин, born October 10, 1958, in Leningrad, Soviet Union) is a mathematical physicist, currently a professor of mathematics at Tsinghua University, China and a professor of mathematical physics at the University of Amsterdam (Korteweg-de Vries Institute for Mathematics). He is also a professor emeritus at the University of California, Berkeley. His research is in the fields of low-dimensional topology, representation theory, and quantum groups. His major contributions are in the theory of quantum integrable systems, in representation theory of quantum groups and in quantum topology. He and Vladimir Turaev constructed invariants of 3-manifolds which are expected to describe quantum Chern–Simons field theory introduced by Edward Witten. He earned his bachelor's degree and master's degree from Leningrad State University in 1982, and his Ph.D. from the Steklov Mathematical Institute in 1984. He gave a plenary lecture at the International Congress of Mathematicians in 2010. He was named a Fellow of the American Mathematical Society, in the 2022 class of fellows, "for contributions to the theory of quantum groups, integrable systems, topology, and quantum physics". In 2022, Reshetikhin received the inaugural Weyl-Wigner Award from ICGTMP.

Illustrations

Worked examples

Example 1 — a first encounter with Nicolai Reshetikhin

Start with the simplest possible case. Write down what Nicolai Reshetikhin 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 Nicolai Reshetikhin 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 Nicolai Reshetikhin 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 Nicolai Reshetikhin

In research: Nicolai Reshetikhin 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 Nicolai Reshetikhin 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: Nicolai Reshetikhin is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1958 births, 20th-century Russian mathematicians, 21st-century Russian mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Nicolai Reshetikhin 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 Nicolai Reshetikhin in 20 minutes

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

Frequently asked questions

What is Nicolai Reshetikhin in simple terms?

Why does Nicolai Reshetikhin 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 Nicolai Reshetikhin?

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 Nicolai Reshetikhin.