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SUMMARY:An introduction to quantum graphs and their spectral geometry\, wi
 th some open questions - Delio Mugnolo
DTSTART:20250313T150000Z
DTEND:20250313T160000Z
UID:TALK229231@talks.cam.ac.uk
CONTACT:Matthew Colbrook
DESCRIPTION:Quantum graphs are (usually self-adjoint) second-order differe
 ntial operators over collections of intervals that are glued at their endp
 oints ("metric graphs"). We survey recent and past advances in quantum gra
 ph eigenvalue estimates\, focusing on how geometry\, topology\, and diffus
 ion-transport phenomena interact. Specifically\, we examine surgery techni
 ques—localized graph modifications—to manipulate eigenvalues. We also 
 explore transport and transport-diffusion equations on directed graphs\, h
 ighlighting how directional flow and non-symmetric operators impact spectr
 al properties. We discuss adapting surgery techniques to control these eff
 ects\, emphasizing the link between edge transmission/boundary conditions\
 , diffusion-transport dynamics\, and resulting eigenvalues.
LOCATION:Centre for Mathematical Sciences\, MR14
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