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SUMMARY:Tsachik Gelander: "Infinite volume and infinite injectivity radius
"
DTSTART;VALUE=DATE-TIME:20210428T120000Z
DTEND;VALUE=DATE-TIME:20210428T130000Z
DTSTAMP;VALUE=DATE-TIME:20210508T105008Z
UID:indico-event-6617@indico.math.cnrs.fr
DESCRIPTION:We prove the following conjecture of Margulis. Let G be a high
er rank simple Lie group and let Λ ≤ G be a discrete subgroup of infini
te covolume. Then\, the locally symmetric space Λ\\G/K admits injected ba
lls of any radius. This can be considered as a geometric interpretation of
the celebrated Margulis normal subgroup theorem. However\, it applies to
general discrete subgroups not necessarily associated to lattices. Yet\, t
he result is new even for subgroups of infinite index of lattices. We esta
blish similar results for higher rank semisimple groups with Kazhdan’s p
roperty (T). We prove a stiffness result for discrete stationary random su
bgroups in higher rank semisimple groups and a stationary variant of the S
tuck–Zimmer theorem for higher rank semisimple groups with property (T).
We also show that a stationary limit of a measure supported on discrete s
ubgroups is almost surely discrete.\n\n \n\nThis is a joint work with Mik
olaj Fraczyk.\n\nhttps://indico.math.cnrs.fr/event/6617/
LOCATION:UMPA 435
URL:https://indico.math.cnrs.fr/event/6617/
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