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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Spectral Stability of Persistent Laplacians - Arne
Wolf (Imperial College London)
DTSTART;TZID=Europe/London:20240801T134500
DTEND;TZID=Europe/London:20240801T141000
UID:TALK219646AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/219646
DESCRIPTION:It is well-known that the kernel of the graph Lapl
acian captures the topological properties (number
of cycles and connected components) of a graph. In
a similar fashion\, the kernel of a persistent La
placian captures the information contained in the
persistent homology of a given simplicial complex.
Our main goal is to understand what we can deduce
from the remaining eigenvalues and -vectors in th
e more general cellular sheaf setting\, which theo
retically incorporate further information of the f
aces of a simplicial complex. In this talk\, I wil
l discuss work in progress towards this aim and pr
esent a recently-established theoretical foundatio
n for this goal\, where we show that the eigenvalu
es are stable under small perturbation of the shea
f and simplicial complex. The upshot of this resul
t is that we can reasonably assume that the additi
onal information encoded by the other eigenvalues
and -vectors are a faithful representation of othe
r geometric or topological properties of the under
lying simplicial complex\, although precisely what
this information represents remains to be investi
gated (current work in progress proceeds with a ma
chine learning approach). Joint work with Shiv Bha
tia\, Daniel Ruiz Cifuentes\, Jiyu Fan and Anthea
Monod.
LOCATION:External
CONTACT:
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