We present a survey of results on word equations in simple groups, as well as their analogues and generalizations, which were obtained over the past decade using various methods: group-theoretic and coming from algebraic and arithmetic geometry, number theory, dynamical systems and computer algebra. Our focus is on interrelations of these machineries which led to numerous spectacular achievements, including solutions of several long-standing problems.
@article{bwmeta1.element.doi-10_2478_s11533-013-0335-4,
author = {Tatiana Bandman and Shelly Garion and Boris Kunyavski\u\i },
title = {Equations in simple matrix groups: algebra, geometry, arithmetic, dynamics},
journal = {Open Mathematics},
volume = {12},
year = {2014},
pages = {175-211},
zbl = {1294.20056},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0335-4}
}
Tatiana Bandman; Shelly Garion; Boris Kunyavskiĭ. Equations in simple matrix groups: algebra, geometry, arithmetic, dynamics. Open Mathematics, Tome 12 (2014) pp. 175-211. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0335-4/
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