# Geoffrey Janssens: An abudance of free products in GL_n(D)

Predavanje je izjemoma že ta torek ob 16:15. Vljudno vabljeni.

Roman Drnovšek in Primož Moravec

Abstract: Given any field F and a finitely generated subgroup G of GL_n(F), the celebrated Tits alternative says that either G contains a free subgroup or it contains a lot of relations, namely it is solvable (up to finite index). Interestingly, when it exists, Tits proof explains how to construct such a free subgroup via dynamics on some associated geometric space. In this talk we will first give an overview on the alternative and the method of 'playing ping-pong' to construct free products. Thereafter we will consider a conjecture of De la Harpe stating that given any finite subset F in a semisimple Lie group H there exists a ‘y’ in H such that is a free product for all b in F. Moreover, there is densely many such ‘y’. More precisely, the plan is to give an impression of the case of GL_n(F). The latter part is based on joint work with Doryan Temmerman and François Thilmany.