Sabir Gusein-Zade

Sabir Gusein-Zade (2010), El Escorial

Sabir Medgidovich Gusein-Zade (Russian: Сабир Меджидович Гусейн-Заде; born 29 July 1950 in Moscow^[1]) is a Russian mathematician and a specialist in singularity theory and its applications.^[2]

He studied at Moscow State University, where he earned his Ph.D. in 1975 under the joint supervision of Sergei Novikov and Vladimir Arnold.^[3] Before entering the university, he had earned a gold medal at the International Mathematical Olympiad.^[2]

Gusein-Zade co-authored with V. I. Arnold and A. N. Varchenko the textbook Singularities of Differentiable Maps (published in English by Birkhäuser).^[2]

A professor in both the Moscow State University and the Independent University of Moscow, Gusein-Zade also serves as co-editor-in-chief for the Moscow Mathematical Journal.^[4] He shares credit with Norbert A’Campo for results on the singularities of plane curves.^[5][6][7]

Selected publications

• S. M. Gusein-Zade. "Dynkin diagrams for singularities of functions of two variables". Functional Analysis and Its Applications, 1974, Volume 8, Issue 4, pp. 295–300.
• S. M. Gusein-Zade. "Intersection matrices for certain singularities of functions of two variables". Functional Analysis and Its Applications, 1974, Volume 8, Issue 1, pp. 10–13.
• A. Campillo, F. Delgado, and S. M. Gusein-Zade. "The Alexander polynomial of a plane curve singularity via the ring of functions on it". Duke Mathematical Journal, 2003, Volume 117, Number 1, pp. 125–156.
• S. M. Gusein-Zade. "The problem of choice and the optimal stopping rule for a sequence of independent trials". Theory of Probability & Its Applications, 1965, Volume 11, Number 3, pp. 472–476.
• S. M. Gusein-Zade. "A new technique for constructing continuous cartograms". Cartography and Geographic Information Systems, 1993, Volume 20, Issue 3, pp. 167–173.

References

1. Home page of Sabir Gusein-Zade
2. Artemov, S. B.; Belavin, A. A.; Buchstaber, V. M.; Esterov, A. I.; Feigin, B. L.; Ginzburg, V. A.; Gorsky, E. A.; Ilyashenko, Yu. S.; Kirillov, A. A.; Khovanskii, A. G.; Lando, S. K.; Margulis, G. A.; Neretin, Yu. A.; Novikov, S. P.; Shlosman, S. B.; Sossinsky, A. B.; Tsfasman, M. A.; Varchenko, A. N.; Vassiliev, V. A.; Vlăduţ, S. G. (2010), "Sabir Medgidovich Gusein-Zade", Moscow Mathematical Journal, 10 (4).
3. Sabir Gusein-Zade at the Mathematics Genealogy Project
4. Editorial Board (2011), "Sabir Gusein-Zade – 60" (PDF), Anniversaries, TWMS Journal of Pure and Applied Mathematics, 2 (1): 161.
5. Wall, C. T. C. (2004), Singular Points of Plane Curves, London Mathematical Society Student Texts, 63, Cambridge University Press, Cambridge, p. 152, doi:10.1017/CBO9780511617560, ISBN 0-521-83904-1, MR 2107253, An important result, due independently to A'Campo and Gusein-Zade, asserts that every plane curve singularity is equisingular to one defined over ${\mathbb R}$ and admitting a real morsification $f_{t}$ with only 3 critical values.
6. Brieskorn, Egbert; Knörrer, Horst (1986), Plane Algebraic Curves, Modern Birkhäuser Classics, Basel: Birkhäuser, p. vii, doi:10.1007/978-3-0348-5097-1, ISBN 978-3-0348-0492-9, MR 2975988, I would have liked to introduce the beautiful results of A'Campo and Gusein-Zade on the computation of the monodromy groups of plane curves. Translated from the German original by John Stillwell, 2012 reprint of the 1986 edition.
7. Rieger, J. H.; Ruas, M. A. S. (2005), "M-deformations of ${\mathcal {A}}$-simple $\Sigma ^{{n-p+1}}$-germs from $\Bbb R^n$ to ${\mathbb R}^{p},n\geq p$", Mathematical Proceedings of the Cambridge Philosophical Society, 139 (2): 333–349, doi:10.1017/S0305004105008625, MR 2168091, For map-germs very little is known about the existence of M-deformations beyond the classical result by A’Campo and Gusein–Zade that plane curve-germs always have M-deformations.