On conjugacy growth of linear groups
  We investigate the conjugacy growth of finitely generated linear groups. We show that finitely generated non-virtually-solvable subgroups of GL_d have uniform exponential conjugacy growth and in fact that the number of distinct polynomials arising as characteristic polynomials of the elements of the ball of radius n for the word metric has exponential growth rate bounded away from 0 in terms of the dimension d only. 
Emmanuel Breuillard, Yves de Cornulier, Alexander Lubotzky, Chen Meiri
math.GR