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SUMMARY:Graph Joinings\, Graph Isomorphism\, and Reversible Markov Chains 
 - Prof Andrew Nobel\, UNC Chapel Hill
DTSTART:20260304T140000Z
DTEND:20260304T150000Z
UID:TALK244771@talks.cam.ac.uk
CONTACT:Dr Varun Jog
DESCRIPTION:Every weighted\, undirected graph describes a simple random wa
 lk on its vertex set\, which is a reversible Markov chain.  In this talk I
  will describe recent work on graph joinings that leverages this elementar
 y connection\, in conjunction with ideas from optimal transport\, to gain 
 insights into both graph isomorphism and couplings of reversible Markov ch
 ains.  Informally\, a joining of two graphs is a product graph from which 
 the given graphs can be recovered via marginalization.  Given two graphs w
 ith labeled vertices\, the optimal graph joining (OGJ) problem identifies 
 a joining that minimizes the weighted degree of vertex pairs with differen
 t labels. For suitable families of labeled graphs\, including trees and fo
 rests\, OGJ can detect and identify isomorphisms between any two graphs in
  the family.  In a different direction\,  I will describe several results 
 showing how graph joinings yield new insights into the rigidity of reversi
 ble couplings of reversible Markov chains.\n\nJoint work with Yang Xiang\,
  Phuong Hoang\, Bongsoo Yi\, and Kevin McGoff.
LOCATION:MR5\, CMS Pavilion A
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