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UID:www.tcs.tifr.res.in/event/362
DTSTAMP:20230914T125921Z
SUMMARY:Ramanujan Graphs of All Degrees
DESCRIPTION:Speaker: Nikhil Srivastava (Microsoft Research\, India\n#9\, La
velle Road\nBangalore\nKarnataka 560025\n\n\n )\n\nAbstract: \nWe prove t
hat there exist infinite families of bipartite Ramanujan graphs of every d
egree bigger than 2. We do this by proving a variant of a conjecture of Bi
lu and Linial about the existence of good 2-lifts of every graph.\nWe also
construct infinite families of `irregular Ramanujan' graphs\, whose eigen
values are bounded by the spectral radius of their universal cover. Such f
amilies were conjectured to exist by Linial and others. In particular\, we
construct infinite families of (c\,d)-biregular bipartite graphs with all
non-trivial eigenvalues bounded by $\\sqrt{c-1}+\\sqrt{d-1}$\, for all $c
\, d \\geq 3$.\nOur proof exploits a new technique for demonstrating the e
xistence of useful combinatorial objects that we call the "Method of Inter
lacing Polynomials" (joint work with A. Marcus and D. Spielman).\n
URL:https://www.tcs.tifr.res.in/web/events/362
DTSTART;TZID=Asia/Kolkata:20130506T163000
DTEND;TZID=Asia/Kolkata:20130506T173000
LOCATION:AG-80
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