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DTSTART:20240310T070000
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DTSTART:20241103T060000
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DTSTART;TZID=America/Toronto:20250303T113000
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URL:https://uwaterloo.ca/combinatorics-and-optimization/events/algebraic-gr
 aph-theory-theo-mckenzie
SUMMARY:Algebraic Graph Theory-Theo McKenzie
CLASS:PUBLIC
DESCRIPTION:TITLE: : Precise Eigenvalue Location for Random Regular Graphs
 \n\nSPEAKER:\n Theo McKenzie\n\nAFFILIATION:\n Stanford University\n\nLOCA
 TION:\n Please contact Sabrina Lato for Zoom link.\n\nABSTRACT:The spect
 ral theory of regular graphs has broad applications\nin theoretical comput
 er science\, statistical physics\, and other areas\nof mathematics. Graphs
  with optimally large spectral gap are known as\nRamanujan graphs. Previou
 s constructions of Ramanujan graphs are based\non number theory and have s
 pecific constraints on the degree and\nnumber of vertices. In this talk\, 
 we show that\, in fact\, most regular\ngraphs are Ramanujan\; specifically
 \, a randomly selected regular graph\nhas a probability of 69% of being Ra
 manujan. We establish this through\na rigorous analysis of the Green’s f
 unction of the adjacency\noperator\, focusing on its behavior under random
  edge switches.
DTSTAMP:20260403T083410Z
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