Jan-Erik Roos

Jan-Erik Ingvar Roos (16 October 1935 – 15 December 2017)^[1] 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.^[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 on 15 December 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 ${\displaystyle \varprojlim }$. 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.