mathematics

Kengo Hirachi

Kengo Hirachi 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 Kengo Hirachi rather than just read about it. In short: Kengo Hirachi (平地健吾 Hirachi Kengo, born 30 November 1964) is a Japanese mathematician, specializing in CR geometry and mathematical analysis. Hirachi received from Osaka University his B.S. in 1987, his M.S. in 1989, and his Dr.Sci., advised by Gen Komatsu, in 1994 with dissertation The second variation of the Bergman kernel for ellipsoids.

Key takeaways

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

Reference excerpt

Kengo Hirachi (平地健吾 Hirachi Kengo, born 30 November 1964) is a Japanese mathematician, specializing in CR geometry and mathematical analysis. Hirachi received from Osaka University his B.S. in 1987, his M.S. in 1989, and his Dr.Sci., advised by Gen Komatsu, in 1994 with dissertation The second variation of the Bergman kernel for ellipsoids. He was a research assistant from 1989 to 1996 and a lecturer from 1996 to 2000 at Osaka University. He was an associate professor from 2000 to 2010 and a full professor from 2010 to the present at the University of Tokyo. He was a visiting professor at the Mathematical Sciences Research Institute from October 1995 to September 1996, at the Erwin Schrödinger Institute for Mathematical Physics from March 2004 to April 2004, at Princeton University from October 2004 to July 2005, and at the Institute for Advanced Study from January 2009 to April 2009.

Hirachi’s work employs a wide range of tools in geometry and analysis, including several complex variables, the complex Monge-Ampère equation, microlocal analysis, parabolic invariant theory, explicit computations, and computer algebra packages. In a paper in the Annals of Mathematics (2000) Hirachi constructed CR invariants of strongly pseudoconvex boundaries via a deep study of the logarithmic singularity of the Bergman kernel. He has proved various results linking the Bergman and Szegő kernels, and he has made significant progress to a program in which the Bergman kernel function plays a role analogous to the heat kernel of Riemannian geometry.

Awards and honors Takebe Senior Prize (1999) of the Mathematical Society of Japan Geometry Prize (2003) of the Mathematical Society of Japan Stefan Bergman Prize (2006) Inoue Prize for Science (2012) Invited lecture at ICM, Seoul 2014

References

External links Kengo Hirachi -- Bibliography, U. of Tokyo website ICM2014 VideoSeries IL8.3 : Kengo Hirachi on Aug14Thu - YouTube

Worked examples

Example 1 — a first encounter with Kengo Hirachi

Start with the simplest possible case. Write down what Kengo Hirachi 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 Kengo Hirachi 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 Kengo Hirachi 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 Kengo Hirachi

In research: Kengo Hirachi 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 Kengo Hirachi 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: Kengo Hirachi is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1964 births, 20th-century Japanese mathematicians, 21st-century Japanese mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Kengo Hirachi 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 Kengo Hirachi in 20 minutes

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

Frequently asked questions

What is Kengo Hirachi in simple terms?

Why does Kengo Hirachi 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 Kengo Hirachi?

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 Kengo Hirachi.