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SUMMARY:Matthew Conder (University of Auckland)
DTSTART:20221124T230000Z
DTEND:20221125T000000Z
DTSTAMP:20260423T035707Z
UID:SiN/49
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SiN/49/">Two
 -generator subgroups of SL2 over local fields</a>\nby Matthew Conder (Univ
 ersity of Auckland) as part of Symmetry in Newcastle\n\n\nAbstract\nIn thi
 s talk\, we will give an overview of some results and open problems relati
 ng to two-generator subgroups of SL2 over a local field K. We first consid
 er the archimedean setting\, where certain discrete and/or free two-genera
 tor subgroups of SL(2\,R) and SL(2\,C) can be identified by investigating 
 their respective actions by Möbius transformations on the upper half plan
 e and Riemann sphere. We then outline some recent results in the non-archi
 medean setting\, obtained by studying the analogous action of SL(2\,K) by 
 isometries on the corresponding Bruhat-Tits tree. Finally\, we discuss an 
 application of this work to the problem of deciding whether a two-generato
 r subgroup of SL(2\,K) is dense.\n
LOCATION:https://researchseminars.org/talk/SiN/49/
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