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DTSTART:20191027T020000
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UID:calendar.97164.field_date.0@mathematics.huji.ac.il
DTSTAMP:20210126T214504Z
CREATED:20191128T230014Z
DESCRIPTION:Date: \n\n2:30pm to 3:30pm\n\n\n\n\nSee also: Number Theory &
Algebraic Geometry\, Events & Seminars\, SeminarsLocation: \n\nRoss 70\n
\n\n\n Title: Ramanujan Conjectures\, Density Hypotheses and Applications
for Arithmetic Groups.\nAbstract: The Generalized Ramanujan Conjecture (GR
C) for GL(n) is a central open problem in modern number theory. Its resolu
tion is known to yield applications in many fields\, such as: Diophantine
approximation and arithmetic groups. For instance\, Deligne's proof of the
Ramanujan-Petersson conjecture for GL(2) was a key ingredient in the work
of Lubotzky\, Phillips and Sarnak on Ramanujan graphs.\nOne can also stat
e analogues (Naive) Ramanujan Conjectures (NRC) for other reductive groups
\, G\, whose validity would imply various applications for the arithmetic
congruence subgroups associated to G. However\, already in the 70's Howe a
nd Piatetski-Shapiro proved that the (NRC) fails even in the case of class
ical split groups.\nIn the 90's Sarnak-Xue put forth the conjecture that a
Density Hypothesis version of the (NRC) should hold\, and that these Dens
ity Hypotheses can serve as a replacement of the (NRC) in many application
s.\nIn this talk I will describe how to prove such Density Hypotheses for
certain classical groups\, by invoking deep and recent results coming from
the Langlands program. Finally\, we shall end with some applications of t
hese Density Hypotheses\, such as bounding the betti numbers of congruence
hyperbolic manifolds\, proving a strengthened version of a conjecture att
ribute to Gromov.\n\n Export\n \n\n \nsubscribe iCal
DTSTART;TZID=Asia/Jerusalem:20191230T143000
DTEND;TZID=Asia/Jerusalem:20191230T153000
LAST-MODIFIED:20191128T230014Z
SUMMARY:NT Seminar - Shai Evra
URL;TYPE=URI:https://mathematics.huji.ac.il/event/nt-seminar-shai-evra
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