Discrete and free 2-generated subgroups of SL(2,R)

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• Matthew Conder, University of Cambridge
• Friday 02 March 2018, 15:00-16:00
• CMS, MR14.

If you have a question about this talk, please contact Nicolas Dupré.

The Tits alternative states that any finitely generated linear group either contains a soluble finite index subgroup or contains a free subgroup of rank 2. This helps to motivate the following: given any 2-generated subgroup of SL(2,R), can one determine if this subgroup is free (of rank 2)? This remains an open question, however a 2014 paper of Eick, Kirschmer and Leedham-Green presents an algorithm (which follows from the work of others) to check whether such a group is discrete and free. In this talk I will discuss the details of this algorithm and outline some possibilities for future work in this area.

This talk is part of the Junior Algebra/Logic/Number Theory seminar series.

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