# Jan-Erik Roos

**Jan-Erik Ingvar Roos** (October 16, 1935 – December 15, 2017)^{[1]} was a Swedish mathematician.

He was born in Halmstad, in the province of Halland on the Swedish west coast.^{[2]} Roos enrolled at Lund University in 1954, and started studying mathematics with Lars Gårding in 1957.^{[3]} Under Gårding's direction he wrote a thesis on ordinary differential equation, and graduated in 1958 with a licentiate degree.^{[2]}^{[4]} Later that year he went to Paris on a doctoral scholarship;^{[3]} 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.^{[5]} 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.^{[3]}

Upon his return to Sweden, Roos was appointed Professor of Mathematics at Stockholm University in 1970, and started building a strong algebra school.^{[2]} He was elected to the Royal Swedish Academy of Sciences in 1980 and was its President from 1980 to 1982.^{[6]} While serving on the Academy, he was on the committees deciding the Rolf Schock Prizes in Mathematics^{[7]} and the Crafoord Prize in Astronomy and Mathematics.^{[8]}

Roos made important contributions to homological algebra, and did extensive computer-assisted studies of Hilbert–Poincaré series and their rationality.^{[9]} 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.^{[10]}

He died December 15, 2017 at his home in Uppsala^{[2]} and is buried at the Uppsala old cemetery.

## Publications[]

- Roos, Jan-Erik (1961). "Sur les foncteurs dérivés de . 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. - 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. doi:10.1216/JCA-2010-2-4-473. MR 2753719.

## References[]

**^**Persson, Ulf (15 February 2018). "Jan-Erik Roos 16/10/1935 – 15/12/2017" (PDF).*Bulletinen*(in Swedish): 3–6. Retrieved 3 June 2020.- ^
^{a}^{b}^{c}^{d}"Jan-Erik Roos: 1935–2017" (PDF).*London Mathematical Society Newsletter*.**477**: 45. 2018. MR 3837430. - ^
^{a}^{b}^{c}Almkvistl, Gert (15 February 2018). "My friend Jan-Erik Roos" (PDF).*Bulletinen*(in Swedish): 10–13. Retrieved 4 June 2020. **^**Jan-Erik Roos at the Mathematics Genealogy Project**^**Laudal, Olav Arnfinn (15 February 2018). "Jan Erik Roos in Paris" (PDF).*Bulletinen*(in Swedish): 6–10. Retrieved 3 June 2020.**^**Roos, Jan-Erik (June 2012). "Torsten Ekedahl" (PDF).*European Mathematical Society Newsletter*.**84**: 16–18. Retrieved 4 June 2020.**^**"Rolf Schock – uniting philosophy, mathematics, music and art".*news.cision.com*. 13 February 2014. Retrieved 3 June 2020.**^**"The Crafoord Prize in Mathematics and Astronomy 2008".*crafoordprize.se*. 17 January 2008. Retrieved 3 June 2020.**^**Avramov, Luchezar L. (2002). "The work of Jan-Erik Roos on the cohomology of commutative rings".*Homology, Homotopy and Applications*.**4**(2): 1–16. doi:10.4310/HHA.2002.v4.n2.a1. ISSN 1532-0073. MR 1918181. Zbl 1003.01010.**^**Lambe, Larry; Löfwall, Clas (eds.). "The Roos Festschrift volumes 1 and 2".*Homology, Homotopy and Applications*.**4**(2): ii–vi, 1–225 and 227–437. MR 1918180. and MR1918521

- 1935 births
- 2017 deaths
- 20th-century Swedish mathematicians
- 21st-century Swedish mathematicians
- Algebraists
- Members of the Royal Swedish Academy of Sciences
- Stockholm University faculty
- Lund University alumni
- People from Halmstad
- Swedish expatriates in France
- Burials at Uppsala old cemetery
- European mathematician stubs
- Swedish scientist stubs