University of Cambridge > Talks.cam > Junior Algebra/Logic/Number Theory seminar > Discrete and free two-generated subgroups of SL2

Discrete and free two-generated subgroups of SL2

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  • UserMatthew Conder, University of Cambridge
  • ClockFriday 25 January 2019, 15:00-16:00
  • HouseCMS, MR14.

If you have a question about this talk, please contact Stacey Law.

Two-generated subgroups of SL(2,R) have been widely studied in the literature, using the action of SL(2,R) on the hyperbolic plane via Möbius transformations. In particular, there exists a practical algorithm which, given any two elements of SL(2,R), determines after finitely many steps whether or not the subgroup they generate is discrete and free of rank two. Does such an algorithm exist for SL2 defined over other locally compact fields? In this talk we answer this question for the case of a non-archimedean local field K. Using the action of the group SL(2,K) on the Bruhat-Tits tree, we construct an original and practical algorithm which determines after finitely many steps whether or not any given two-generated subgroup of SL(2,K) is discrete and free of rank two.

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

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