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SUMMARY:Spectral expansion in random regular graphs - Ewan Cassidy (Univer
 sity of Cambridge)
DTSTART:20251105T133000Z
DTEND:20251105T143000Z
UID:TALK237817@talks.cam.ac.uk
CONTACT:Julia Wolf
DESCRIPTION:Fixed-degree expanders are sparse yet highly connected graphs.
  This quality is captured by their spectral gap -- the difference between 
 the largest and second largest eigenvalues of their adjacency\nmatrix. A c
 elebrated result of Friedman states that a random d-regular graph on n ver
 tices is a near-optimal expander with high probability. I will discuss a g
 eneralization of this result to a regime where the number of vertices grow
 s quasi-exponentially in n. The proof draws on ideas from representation t
 heory and considerations of word maps on the symmetric group.
LOCATION:MR4\, CMS
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