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CATEGORIES:Applied and Computational Analysis
SUMMARY:An introduction to quantum graphs and their spectr
 al geometry\, with some open questions - Delio Mug
 nolo
DTSTART;TZID=Europe/London:20250313T150000
DTEND;TZID=Europe/London:20250313T160000
UID:TALK229231AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/229231
DESCRIPTION:Quantum graphs are (usually self-adjoint) second-o
 rder differential operators over collections of in
 tervals that are glued at their endpoints ("metric
  graphs"). We survey recent and past advances in q
 uantum graph eigenvalue estimates\, focusing on ho
 w geometry\, topology\, and diffusion-transport ph
 enomena interact. Specifically\, we examine surger
 y techniques—localized graph modifications—to mani
 pulate eigenvalues. We also explore transport and 
 transport-diffusion equations on directed graphs\,
  highlighting how directional flow and non-symmetr
 ic operators impact spectral properties. We discus
 s adapting surgery techniques to control these eff
 ects\, emphasizing the link between edge transmiss
 ion/boundary conditions\, diffusion-transport dyna
 mics\, and resulting eigenvalues.
LOCATION:Centre for Mathematical Sciences\, MR14
CONTACT:Matthew Colbrook
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