mathematics

Patrick Dehornoy

Patrick Dehornoy 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 Patrick Dehornoy rather than just read about it. In short: Patrick Dehornoy (11 September 1952 – 4 September 2019) was a mathematician at the University of Caen Normandy who worked on set theory and group theory. Early life and education Dehornoy was born on 11 September 1952 in Rouen, France.

Key takeaways

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

Reference excerpt

Patrick Dehornoy (11 September 1952 – 4 September 2019) was a mathematician at the University of Caen Normandy who worked on set theory and group theory.

Early life and education Dehornoy was born on 11 September 1952 in Rouen, France. He graduated from the Lycée Pierre-Corneille in 1971. He studied at the École normale supérieure from 1971 to 1975 and completed his Ph.D. in 1978 at the University of Paris, with a thesis written under the direction of Kenneth Walter McAloon.

Career Dehornoy was a researcher at the French National Centre for Scientific Research (CNRS) from 1975 to 1982. He was at the University of Caen Normandy as a Professor from 1983 to 2017 and as an Emeritus Professor from 2017 until his death. From 2009 to 2013, he was an adjunct scientific director of the Institut national des sciences mathématiques et de leurs interactions (INSMI) at the CNRS. Dehornoy died on 4 September 2019 in Villejuif, France at the age of 66.

Research Dehornoy found one of the first applications of large cardinals to algebra by constructing a certain left-invariant total order, called the Dehornoy order, on the braid group. In his later career, he was a major contributor to the theory of braid groups, including creating a fast algorithm for comparing braids, and was one of the main contributors to the development of Garside methods.

Awards In 1999, Dehornoy received the Ferran Sunyer i Balaguer Prize. In 2002, he was elected a senior member of the Institut Universitaire de France (renewed in 2007). In 2005, he received the Prix Langevin of the French Academy of Sciences. In 2014, he received the EMS Monograph Award for his book Foundations of Garside Theory.

Selected publications Dehornoy, Patrick (1994), "Braid groups and left distributive operations", Transactions of the American Mathematical Society, 345 (1): 115–150, doi:10.2307/2154598, ISSN 0002-9947, JSTOR 2154598, MR 1214782 Dehornoy, Patrick (1995), "From large cardinals to braids via distributive algebra", Journal of Knot Theory and Its Ramifications, 4 (1): 33–79, doi:10.1142/S0218216595000041, ISSN 0218-2165, MR 1321290 Dehornoy, Patrick; Dynnikov, Ivan; Rolfsen, Dale; Wiest, Bert (2008), Ordering braids, Mathematical Surveys and Monographs, vol. 148, Providence, R.I.: American Mathematical Society, ISBN 978-0-8218-4431-1, MR 2463428 Dehornoy, Patrick; Digne, François; Godelle, Eddy; Krammer, Daan; Michel, Jean (2015), Foundations of Garside theory, EMS Tracts in Mathematics, vol. 22, Zürich: European Mathematical Society, ISBN 978-3-03719-139-2, MR 3362691 Dehornoy, Patrick (2017), "Multifraction reduction (II): conjectures for Artin–Tits groups", Journal of Combinatorial Algebra, 1 (3): 229–287, arXiv:1606.08995, doi:10.4171/JCA/1-3-1, ISSN 2415-6302, MR 3681576, S2CID 119604700

References

External links "Home page of Patrick Dehornoy". Archived from the original on 5 September 2019. Retrieved 4 January 2019.

Illustrations

Worked examples

Example 1 — a first encounter with Patrick Dehornoy

Start with the simplest possible case. Write down what Patrick Dehornoy 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 Patrick Dehornoy 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 Patrick Dehornoy 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 Patrick Dehornoy

In research: Patrick Dehornoy 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 Patrick Dehornoy 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: Patrick Dehornoy is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1952 births, 2019 deaths, 20th-century French mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Patrick Dehornoy 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 Patrick Dehornoy in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Patrick Dehornoy 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.
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Frequently asked questions

What is Patrick Dehornoy in simple terms?

Patrick Dehornoy (11 September 1952 – 4 September 2019) was a mathematician at the University of Caen Normandy who worked on set theory and group theory. Early life and education Dehornoy was born on 11 September 1952 in Rouen, France.

Why does Patrick Dehornoy 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 Patrick Dehornoy?

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 Patrick Dehornoy.