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SUMMARY:Arielle Leitner (Weizmann Institute of Science)
DTSTART:20201210T130000Z
DTEND:20201210T140000Z
DTSTAMP:20260423T005757Z
UID:AGNTISTA/18
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AGNTISTA/18/
 ">Limits of the diagonal Cartan subgroup in SL(n\,R) and SL(n\, Q_p)</a>\n
 by Arielle Leitner (Weizmann Institute of Science) as part of Algebraic Ge
 ometry and Number Theory seminar - ISTA\n\n\nAbstract\nA conjugacy limit g
 roup is the limit of a sequence of conjugates of the positive diagonal Car
 tan subgroup\, C \\leq SL(n) in the Chabauty topology.   Over R\, the grou
 p C is naturally associated to a projective n-1 simplex.  We can compute t
 he conjugacy limits of C by collapsing the n-1 simplex in different ways. 
  In low dimensions\, we enumerate all possible ways of doing this.  In hig
 her dimensions we show there are infinitely many non-conjugate limits of C
 . \nIn the Q_p case\, SL(n\,Q_p) has an associated p+1 regular affine buil
 ding.  (We'll give a gentle introduction to buildings in the talk).  The g
 roup C stabilizes an apartment in this building\, and limits are contained
  in the parabolic subgroups stabilizing the facets in the spherical buildi
 ng at infinity. There is a strong interplay between the conjugacy limit gr
 oups and the geometry of the building\, which we exploit to extend some of
  the results above.  The Q_p part is joint work with Corina Ciobotaru and 
 Alain Valette.\n
LOCATION:https://researchseminars.org/talk/AGNTISTA/18/
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