mathematics

Hiraku Nakajima

Hiraku Nakajima 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 Hiraku Nakajima rather than just read about it. In short: Hiraku Nakajima (Japanese: 中島啓 Nakajima Hiraku; born November 30, 1962) is a Japanese mathematician, and a professor of the Kavli Institute for the Physics and Mathematics of the Universe at the University of Tokyo. He is International Mathematical Union president for the 2023–2026 term.

Key takeaways

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

Reference excerpt

Hiraku Nakajima (Japanese: 中島啓 Nakajima Hiraku; born November 30, 1962) is a Japanese mathematician, and a professor of the Kavli Institute for the Physics and Mathematics of the Universe at the University of Tokyo. He is International Mathematical Union president for the 2023–2026 term. He obtained his Ph.D. from the University of Tokyo in 1991. In 2002 he was plenary speaker at the International Congress of Mathematicians in Beijing. He won the 2003 Cole Prize in algebra for his work on representation theory and geometry. He proved Nekrasov's conjecture.

Biography 1985 - BA from the University of Tokyo 1987 - MA from the University of Tokyo, and became a research associate at the University of Tokyo 1991 - PhD from the University of Tokyo 1992 - Associate professor at Tohoku University 1995 - Associate professor at the University of Tokyo 1997 - Associate professor at Kyoto University 2000 - Full professor at Kyoto University 2018 - Full professor at Kavli Institute for the Physics and Mathematics of the Universe

Awards and prizes 1997 - Geometry Prize of the Mathematical Society of Japan 2000 - Spring Prize of the Mathematical Society of Japan 2003 - Cole Prize in algebra of the American Mathematical Society 2005 - JSPS prize of the Japan Society for the Promotion of Science 2014 - Japan Academy Prize

Notable publications Shigetoshi Bando, Atsushi Kasue, and Hiraku Nakajima. On a construction of coordinates at infinity on manifolds with fast curvature decay and maximal volume growth. Invent. Math. 97 (1989), no. 2, 313–349. doi:10.1007/BF01389045 Hiraku Nakajima. Instantons on ALE spaces, quiver varieties, and Kac-Moody algebras. Duke Math. J. 76 (1994), no. 2, 365–416. doi:10.1215/S0012-7094-94-07613-8 Hiraku Nakajima. Heisenberg algebra and Hilbert schemes of points on projective surfaces. Ann. of Math. (2) 145 (1997), no. 2, 379–388. doi:10.2307/2951818 , arXiv:alg-geom/9507012 Hiraku Nakajima. Quiver varieties and Kac-Moody algebras. Duke Math. J. 91 (1998), no. 3, 515–560. doi:10.1215/S0012-7094-98-09120-7 Hiraku Nakajima. Quiver varieties and finite-dimensional representations of quantum affine algebras. J. Amer. Math. Soc. 14 (2001), no. 1, 145–238. doi:10.1090/S0894-0347-00-00353-2

External links Nakajima's homepage "2003 Cole Prize in Algebra" (PDF), Notices of the American Mathematical Society, 50 (4): 468–469, 2003

Worked examples

Example 1 — a first encounter with Hiraku Nakajima

Start with the simplest possible case. Write down what Hiraku Nakajima 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 Hiraku Nakajima 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 Hiraku Nakajima 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 Hiraku Nakajima

In research: Hiraku Nakajima 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 Hiraku Nakajima 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: Hiraku Nakajima is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1962 births, 20th-century Japanese mathematicians, 21st-century Japanese mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Hiraku Nakajima 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 Hiraku Nakajima in 20 minutes

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

Frequently asked questions

What is Hiraku Nakajima in simple terms?

Why does Hiraku Nakajima 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 Hiraku Nakajima?

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 Hiraku Nakajima.