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SUMMARY:Gergely Harcos (Rényi Institute\, Budapest\, Hungary)
DTSTART:20200703T110000Z
DTEND:20200703T120000Z
DTSTAMP:20260423T021346Z
UID:NTdL/10
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NTdL/10/">Th
 e density hypothesis for horizontal families of lattices</a>\nby Gergely H
 arcos (Rényi Institute\, Budapest\, Hungary) as part of Number theory dur
 ing lockdown\n\n\nAbstract\nLet G be a semisimple real Lie group without c
 ompact factors and\nGamma an arithmetic lattice in G. Sarnak and Xue formu
 lated a conjecture\non the multiplicity with which a given irreducible uni
 tary representation\nof G occurs in the right regular representation of G 
 on L^2(Gamma\\G). It\nis known for the groups SL(2\,R) and SL(2\,C) by the
  work of Sarnak-Xue\n(1991) and Huntley-Katznelson (1993). I will report o
 n recent joint work\nwith Mikołaj Frączyk\, Péter Maga\, and Djordje Mi
 lićević\, where we prove a\nstrong\, effective version of the conjecture
  for products of SL(2\,R)'s and\nSL(2\,C)'s. We consider congruence lattic
 es coming from quaternion algebras\nover number fields of bounded degree\,
  and we address uniformity in all\narchimedean parameters.\n
LOCATION:https://researchseminars.org/talk/NTdL/10/
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