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UID:node-3034956@mathematics.huji.ac.il
DTSTAMP:20210520T130000Z
DTSTART:20210520T130000Z
DTEND:20210520T141500Z
SUMMARY:Basic Notions: Alex Lubotzky (HUJI) "From Ramanujan graphs to Ramanujan complexes".
DESCRIPTION:Ramanujan graphs are k-regular graphs with all nontrivial eigenvalues are \nbounded ( in absolute value) by 2SR(k-1). Theyare optimal expanders (from \nspectral point of view). Explicit constructions ofsuch graphs were given in \nthe 80's as quotients of the Bruhat-Tits treeassociated with GL(2) over a \nlocal field F, by the action of suitablecongruence subgroups of arithmetic \ngroups.\n\nThespectral bound was proved using works of Hecke, Deligne and Drinfeld on \nthe"Ramanujan conjecture" in the theory ofautomorphic forms.\n\nThe work of Lafforgue, extending Drinfeld from GL(2) to GL(n),opened the door \nfor the construction of Ramanujan complexes as quotients of theBruhat-Tits \nbuildings associated with GL(n) over F.\n\nThis way onegets finite simplical complxes which on one hand are "random like \n''and at the same time have strong symmetries. These seemingly \ncontradictingproperties make them very useful for constructions of \nvariousexternal objects.\n\nVarious applications have been found in combinatorics, coding t...
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