mathematics

Paul Biran

Paul Biran 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 Paul Biran rather than just read about it. In short: Paul Ian Biran (Hebrew: פאול בירן; born 25 February 1969) is an Israeli mathematician. He holds a chair at ETH Zurich.

Key takeaways

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

Reference excerpt

Paul Ian Biran (Hebrew: פאול בירן; born 25 February 1969) is an Israeli mathematician. He holds a chair at ETH Zurich. His research interests include symplectic geometry and algebraic geometry.

Education Born in Romania in 1969, Biran's family moved to Israel in 1971. He attended Tel Aviv University, where he earned his Bachelor's degree in 1994 and Ph.D. in 1997 under supervision of Leonid Polterovich (thesis: Geometry of Symplectic Packing).

Career From 1997 to 1999, Biran was a "Szego Assistant Professor" at Stanford University. At Tel Aviv University, he was a lecturer from 1997 to 2001, a senior lecturer from 2001 to 2005, an associate professor in 2005, and a full professor in 2008. In 2009, Biran became a full professor of mathematics at ETH Zurich.

Awards Biran was awarded the Oberwolfach Prize in 2003, the EMS Prize in 2004, and the Erdős Prize in 2006. In 2013 he became a member of the German Academy of Sciences Leopoldina.

Publications Salamon, Dietmar; Polterovich, Leonid; Biran, Paul (2003). "Propagation in Hamiltonian dynamics and relative symplectic homology". Duke Mathematical Journal. 119 (1): 65–118. arXiv:math/0108134. doi:10.1215/s0012-7094-03-11913-4. MR 1991647. S2CID 17473995. Biran, Paul; Cornea, Octav (2009). "Rigidity and uniruling for Lagrangian submanifolds". Geometry & Topology. 13 (5): 2881–2989. arXiv:0808.2440. doi:10.2140/gt.2009.13.2881. MR 2546618.

Illustrations

Worked examples

Example 1 — a first encounter with Paul Biran

Start with the simplest possible case. Write down what Paul Biran 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 Paul Biran 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 Paul Biran 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 Paul Biran

In research: Paul Biran 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 Paul Biran 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: Paul Biran is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1969 births, 21st-century Israeli mathematicians, Academic staff of ETH Zurich, so understanding it makes those chapters shorter.
In everyday life: Look for Paul Biran 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 Paul Biran in 20 minutes

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

Frequently asked questions

What is Paul Biran in simple terms?

Paul Ian Biran (Hebrew: פאול בירן; born 25 February 1969) is an Israeli mathematician. He holds a chair at ETH Zurich.

Why does Paul Biran 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 Paul Biran?

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 Paul Biran.