mathematics

Tomoyuki Arakawa

Tomoyuki Arakawa 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 Tomoyuki Arakawa rather than just read about it. In short: Tomoyuki Arakawa (Japanese: 荒川知幸; born 22 May 1968) is a Japanese mathematician, mathematical physicist, and a professor at the RIMS of the Kyoto University. His research interests are representation theory and vertex algebras and he is known especially for the work in W-algebras.

Key takeaways

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

Reference excerpt

Tomoyuki Arakawa (Japanese: 荒川知幸; born 22 May 1968) is a Japanese mathematician, mathematical physicist, and a professor at the RIMS of the Kyoto University. His research interests are representation theory and vertex algebras and he is known especially for the work in W-algebras. He obtained his PhD from the University of Nagoya in 1999. In 2018 he was invited speaker at the International Congress of Mathematicians in Rio de Janeiro. He won the MSJ Autumn Prize in 2017 for his work on representation theory of W-algebras.

Selected publications Arakawa, Tomoyuki (1 August 2007). "Representation theory of W-algebras". Inventiones Mathematicae. 169 (2): 219–320. doi:10.1007/s00222-007-0046-1. hdl:10935/1423. ISSN 1432-1297. S2CID 122047968. Arakawa, Tomoyuki (2015). "Rationality of W-algebras: principal nilpotent cases". Annals of Mathematics. 182 (2): 565–604. arXiv:1211.7124. doi:10.4007/annals.2015.182.2.4. ISSN 0003-486X. JSTOR 24523343. S2CID 53477362. Arakawa, Tomoyuki; Creutzig, Thomas; Linshaw, Andrew R. (1 October 2019). "W-algebras as coset vertex algebras". Inventiones Mathematicae. 218 (1): 145–195. arXiv:1801.03822. Bibcode:2019InMat.218..145A. doi:10.1007/s00222-019-00884-3. ISSN 1432-1297. S2CID 253745764.

References

External links Personal website

Worked examples

Example 1 — a first encounter with Tomoyuki Arakawa

Start with the simplest possible case. Write down what Tomoyuki Arakawa 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 Tomoyuki Arakawa 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 Tomoyuki Arakawa 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 Tomoyuki Arakawa

In research: Tomoyuki Arakawa 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 Tomoyuki Arakawa 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: Tomoyuki Arakawa is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1968 births, Academic staff of Kyoto University, Asian mathematician stubs, so understanding it makes those chapters shorter.
In everyday life: Look for Tomoyuki Arakawa 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 Tomoyuki Arakawa in 20 minutes

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

Frequently asked questions

What is Tomoyuki Arakawa in simple terms?

Why does Tomoyuki Arakawa 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 Tomoyuki Arakawa?

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 Tomoyuki Arakawa.