mathematics

Jan-Erik Roos

Jan-Erik Roos 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 Jan-Erik Roos rather than just read about it. In short: Jan-Erik Ingvar Roos (16 October 1935 – 15 December 2017) was a Swedish mathematician whose research interests were in abelian category theory, homological algebra, and related areas. He was born in Halmstad, in the province of Halland on the Swedish west coast.

Key takeaways

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Reference excerpt

Jan-Erik Ingvar Roos (16 October 1935 – 15 December 2017) was a Swedish mathematician whose research interests were in abelian category theory, homological algebra, and related areas. He was born in Halmstad, in the province of Halland on the Swedish west coast. Roos enrolled at Lund University in 1954, and started studying mathematics with Lars Gårding in 1957. Under Gårding's direction he wrote a thesis on ordinary differential equation, and graduated in 1958 with a licentiate degree. Later that year he went to Paris on a doctoral scholarship; there, he gravitated towards the mathematical environment at the Institut Henri Poincaré, and the various seminars held there. After a while, he started attending Alexander Grothendieck's seminar at the Institut des hautes études scientifiques in Bures-sur-Yvette, where he became interested in abstract algebra and algebraic geometry. In 1967 he was invited by Saunders Mac Lane to visit the University of Chicago for three months; Mac Lane was impressed by Roos and later wrote a very positive letter of recommendation for him. Upon his return to Sweden, Roos was appointed Professor of Mathematics at Stockholm University in 1970, and started building a strong algebra school. He was elected to the Royal Swedish Academy of Sciences in 1980 and was its President from 1980 to 1982. While serving on the Academy, he was on the committees deciding the Rolf Schock Prizes in Mathematics and the Crafoord Prize in Astronomy and Mathematics. Roos made important contributions to homological algebra, and did extensive computer-assisted studies of Hilbert–Poincaré series and their rationality. A special issue of the journal Homology, Homotopy and Applications ("The Roos Festschrift volume") was published in 2002, on the occasion of his 65th birthday. He died on 15 December 2017 at his home in Uppsala and is buried at the Uppsala old cemetery.

Publications Roos, Jan-Erik (1961). "Sur les foncteurs dérivés de lim ← {\displaystyle \varprojlim } . Applications". Comptes rendus de l'Académie des Sciences. 252: 3702–3704. MR 0132091. Roos, Jan-Erik (1993). "Commutative non-Koszul algebras having a linear resolution of arbitrarily high order. Applications to torsion in loop space homology". Comptes rendus de l'Académie des Sciences. 316 (11): 1123–1128. MR 1221635. Löfwall, Clas; Roos, Jan-Erik (1997). "A Nonnilpotent 1-2-Presented Graded Hopf Algebra Whose Hilbert Series Converges in the Unit Circle". Advances in Mathematics. 130 (2): 161–200. doi:10.1006/aima.1997.1667. MR 1472316. Roos, Jan-Erik; Sturmfels, Bernd (1998). "A toric ring with irrational Poincaré-Betti series". Comptes rendus de l'Académie des Sciences. 326 (2): 141–146. Bibcode:1998CRASM.326..141R. doi:10.1016/S0764-4442(97)89459-1. MR 1646972. Roos, Jan-Erik (2006). "Derived functors of inverse limits revisited". Journal of the London Mathematical Society. 73 (1): 65–83. doi:10.1112/S0024610705022416. MR 2197371. S2CID 122666355. Roos, Jan-Erik (2008). "The homotopy Lie algebra of a complex hyperplane arrangement is not necessarily finitely presented". Experimental Mathematics. 17 (2): 129–143. arXiv:math/0610126. doi:10.1080/10586458.2008.10129030. MR 2433880. S2CID 7626968. Roos, Jan-Erik (2010). "Three-dimensional manifolds, skew-Gorenstein rings and their cohomology". Journal of Commutative Algebra. 2 (4): 473–499. arXiv:1005.2919. doi:10.1216/JCA-2010-2-4-473. MR 2753719.

References

Worked examples

Example 1 — a first encounter with Jan-Erik Roos

Start with the simplest possible case. Write down what Jan-Erik Roos 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 Jan-Erik Roos 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 Jan-Erik Roos 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 Jan-Erik Roos

In research: Jan-Erik Roos 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 Jan-Erik Roos 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: Jan-Erik Roos is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1935 births, 2017 deaths, 20th-century Swedish mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Jan-Erik Roos 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 Jan-Erik Roos in 20 minutes

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Frequently asked questions

What is Jan-Erik Roos in simple terms?

Why does Jan-Erik Roos 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.

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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 Jan-Erik Roos.