Equations in simple matrix groups: algebra, geometry, arithmetic, dynamics

Tatiana Bandman; Shelly Garion; Boris Kunyavskiĭ

Open Mathematics (2014)

  • Volume: 12, Issue: 2, page 175-211
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Tatiana Bandman, Shelly Garion, and Boris Kunyavskiĭ. "Equations in simple matrix groups: algebra, geometry, arithmetic, dynamics." Open Mathematics 12.2 (2014): 175-211. <http://eudml.org/doc/269029>.

@article{TatianaBandman2014,
abstract = {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.},
author = {Tatiana Bandman, Shelly Garion, Boris Kunyavskiĭ},
journal = {Open Mathematics},
keywords = {Matrix groups; Finite simple groups; Special linear group; Word map; Trace map; Arithmetic dynamics; Periodic points; Finite fields; Lang-Weil estimate; matrix groups; matrix equations; finite simple groups; Ore conjecture; special linear groups; word maps; trace maps; arithmetic dynamics; periodic points; finite fields; Lang-Weil estimates},
language = {eng},
number = {2},
pages = {175-211},
title = {Equations in simple matrix groups: algebra, geometry, arithmetic, dynamics},
url = {http://eudml.org/doc/269029},
volume = {12},
year = {2014},
}

TY - JOUR
AU - Tatiana Bandman
AU - Shelly Garion
AU - Boris Kunyavskiĭ
TI - Equations in simple matrix groups: algebra, geometry, arithmetic, dynamics
JO - Open Mathematics
PY - 2014
VL - 12
IS - 2
SP - 175
EP - 211
AB - 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.
LA - eng
KW - Matrix groups; Finite simple groups; Special linear group; Word map; Trace map; Arithmetic dynamics; Periodic points; Finite fields; Lang-Weil estimate; matrix groups; matrix equations; finite simple groups; Ore conjecture; special linear groups; word maps; trace maps; arithmetic dynamics; periodic points; finite fields; Lang-Weil estimates
UR - http://eudml.org/doc/269029
ER -

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