mathematics

Pierre Schapira (mathematician)

Pierre Schapira (mathematician) 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 Pierre Schapira (mathematician) rather than just read about it. In short: Pierre Schapira (born April 28, 1943) is a French mathematician. He specializes in algebraic analysis, especially Mikio Sato's microlocal analysis, together with the mathematical concepts of sheaves and derived categories.

Key takeaways

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

Reference excerpt

Pierre Schapira (born April 28, 1943) is a French mathematician. He specializes in algebraic analysis, especially Mikio Sato's microlocal analysis, together with the mathematical concepts of sheaves and derived categories. Schapira received his doctorate for work on hyperfunctions. Although these were already in use in France by André Martineau, they were further developed by Schapira and Jacques-Louis Lions. This work earned Shapira an invitation to Kyoto University, where he met Masaki Kashiwara. Together, they developed the microlocal theory of sheaves, and have co-authored many papers spanning several decades. He served as a professor at the Paris 13 University in the 1980s and has been a professor at the Pierre and Marie Curie University since the 1990s. In 1990, he was an invited speaker at the International Congress of Mathematicians in Kyoto, speaking on sheaf theory for partial differential equations. Schapira was inducted as a fellow of the American Mathematical Society with the Society's inaugural class of Fellows in 2013.

See also Mikio Sato Masaki Kashiwara Jean Leray Alexander Grothendieck

References

External links Pierre Schapira's page at Institut de Mathématiques de Jussieu-Paris Rive Gauche Archived 2014-03-22 at the Wayback Machine Videos of Pierre Schapira in the AV-Portal of the German National Library of Science and Technology

Illustrations

Worked examples

Example 1 — a first encounter with Pierre Schapira (mathematician)

Start with the simplest possible case. Write down what Pierre Schapira (mathematician) 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 Pierre Schapira (mathematician) 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 Pierre Schapira (mathematician) 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 Pierre Schapira (mathematician)

In research: Pierre Schapira (mathematician) 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 Pierre Schapira (mathematician) 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: Pierre Schapira (mathematician) is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1943 births, 20th-century French mathematicians, 21st-century French mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Pierre Schapira (mathematician) 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 Pierre Schapira (mathematician) in 20 minutes

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

Frequently asked questions

What is Pierre Schapira (mathematician) in simple terms?

Why does Pierre Schapira (mathematician) 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 Pierre Schapira (mathematician)?

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 Pierre Schapira (mathematician).