mathematics

Kiyoshi Igusa

Kiyoshi Igusa 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 Kiyoshi Igusa rather than just read about it. In short: Kiyoshi Igusa (born November 28, 1949) is a Japanese-American mathematician and a professor at Brandeis University. He works in representation theory and topology.

Key takeaways

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

Reference excerpt

Kiyoshi Igusa (born November 28, 1949) is a Japanese-American mathematician and a professor at Brandeis University. He works in representation theory and topology.

Education and career He studied at the University of Chicago and Princeton University, where he obtained his Ph.D. in 1979, under the direction of Allen Hatcher and Wu-Chung Hsiang. From 1981 to 1983, he was a Sloan Fellow, and since 2012 he is a Fellow of the American Mathematical Society. In 1990, he gave an invited lecture at the International Congress of Mathematicians in Kyoto (Topology Section).

Personal life Igusa's father, Jun-Ichi Igusa, was also a mathematician. Igusa is married to Gordana Todorov, with whom he is a frequent collaborator.

Selected publications Igusa, Kiyoshi; Orr, Kent E. (2001). "Links, pictures and the homology of nilpotent groups". Topology. 40 (6): 1125–1166. doi:10.1016/s0040-9383(00)00002-1. MR 1867241. Igusa, Kiyoshi (2002). Higher Franz-Reidemeister torsion. AMS/IP Studies in Advanced Mathematics. Vol. 31. Providence, RI: American Mathematical Society. ISBN 978-0-8218-3170-0. MR 1945530. Goette, Sebastian; Igusa, Kiyoshi (2014). "Exotic smooth structures on topological fiber bundles II". Transactions of the American Mathematical Society. 366 (2): 791–832. doi:10.1090/s0002-9947-2013-05858-8. MR 3130317. Goodwillie, Thomas; Igusa, Kiyoshi; Ohrt, Christopher (2015). "An equivariant version of Hatcher's G/O construction". Journal of Topology. 8 (3): 675–690. arXiv:1307.5554. doi:10.1112/jtopol/jtv015. MR 3394313. S2CID 119733082.

References

External links Kiyoshi Igusa (Personal Website)

Worked examples

Example 1 — a first encounter with Kiyoshi Igusa

Start with the simplest possible case. Write down what Kiyoshi Igusa 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 Kiyoshi Igusa 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 Kiyoshi Igusa 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 Kiyoshi Igusa

In research: Kiyoshi Igusa 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 Kiyoshi Igusa 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: Kiyoshi Igusa is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1949 births, 20th-century American mathematicians, 21st-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Kiyoshi Igusa 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 Kiyoshi Igusa in 20 minutes

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

Frequently asked questions

What is Kiyoshi Igusa in simple terms?

Kiyoshi Igusa (born November 28, 1949) is a Japanese-American mathematician and a professor at Brandeis University. He works in representation theory and topology.

Why does Kiyoshi Igusa 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 Kiyoshi Igusa?

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 Kiyoshi Igusa.