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SUMMARY:Spectral Stability of Persistent Laplacians - Arne Wolf (Imperial 
 College London)
DTSTART:20240801T124500Z
DTEND:20240801T131000Z
UID:TALK219646@talks.cam.ac.uk
DESCRIPTION:It is well-known that the kernel of the graph Laplacian captur
 es the topological properties (number of cycles and connected components) 
 of a graph. In a similar fashion\, the kernel of a persistent Laplacian ca
 ptures the information contained in the persistent homology of a given sim
 plicial complex. Our main goal is to understand what we can deduce from th
 e remaining eigenvalues and -vectors in the more general cellular sheaf se
 tting\, which theoretically incorporate further information of the faces o
 f a simplicial complex. In this talk\, I will discuss work in progress tow
 ards this aim and present a recently-established theoretical foundation fo
 r this goal\, where we show that the eigenvalues are stable under small pe
 rturbation of the sheaf and simplicial complex. The upshot of this result 
 is that we can reasonably assume that the additional information encoded b
 y the other eigenvalues and -vectors are a faithful representation of othe
 r geometric or topological properties of the underlying simplicial complex
 \, although precisely what this information represents remains to be inves
 tigated (current work in progress proceeds with a machine learning approac
 h). Joint work with Shiv Bhatia\, Daniel Ruiz Cifuentes\, Jiyu Fan and Ant
 hea Monod.
LOCATION:External
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