Discrete and free two-generated subgroups of SL2

Add to your list(s) Download to your calendar using vCal

• Matthew Conder, University of Cambridge
• Friday 25 January 2019, 15:00-16:00
• CMS, 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 and Number Theory seminar series.

This talk is included in these lists:

• All CMS events
• All Talks (aka the CURE list)
• CMS Events
• CMS, MR14
• DPMMS Lists
• DPMMS Pure Maths Seminar
• DPMMS info aggregator
• DPMMS lists
• Hanchen DaDaDash
• Interested Talks
• Junior Algebra and Number Theory seminar
• School of Physical Sciences
• bld31
• ndb35's list

Note that ex-directory lists are not shown.