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SUMMARY:Irreducible discrete subgroups of G × G and ergodicity on the bou
 ndary - Subhadip Dey (Tata Institute of Fundamental Research)
DTSTART:20250903T081500Z
DTEND:20250903T091500Z
UID:TALK233923@talks.cam.ac.uk
DESCRIPTION:Let G be a noncompact simple real Lie group\, and let &Gamma\;
  be an irreducible discrete subgroup of G &times\; G\, i.e. its projection
 s to both factors are dense. For G = SL(2\,R)\, the only known examples ar
 e lattices. We will highlight some questions and present some results show
 ing that certain irreducible groups are subject to strong structural const
 raints. Along the way\, we construct counterexamples to a conjecture of Ma
 rgulis by exhibiting discrete subgroups of infinite covolume in higher-ran
 k simple groups G whose associated locally symmetric spaces admit no nontr
 ivial bounded harmonic functions. We will also discuss examples of two qua
 si-isometric locally symmetric spaces with finitely presented fundamental 
 groups\, where one admits nontrivial bounded harmonic functions while the 
 other does not\, highlighting ergodic properties at infinity.\nThis is all
  based on joint work in progress with Sebastian Hurtado.
LOCATION:Seminar Room 1\, Newton Institute
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