Calendar
Wednesday, February 5, 2025
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All day |
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4:00pm |
02/05/2025 - 4:00pm Let \Gamma be an irreducible lattice in a higher-rank semisimple Lie group. We show that every subgroup of infinite index admits a sequence of conjugates that converge to the trivial group (i.e. eventually intersect trivially every finite set). This significantly strengthens the celebrated normal subgroup theorem of Margulis.
As in classical NST, this result is a consequence of the tension between amenability and property (T) and the proof is more complicated when the ambient Lie group does not have property (T). Most of the works that improved the NST (such as the Stuck–Zimmer theorem and my recent work with M. Fraczyk) assumed property (T). In the recent paper (with Bader and Levit), we established the result in full generality by proving a spectral gap theorem for actions of products of groups, which may replace Kazhdan’s property (T).
Based on a recent joint work with Uri Bader and Arie Levit.
Location:
KT 101
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