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SUMMARY:Luis Scoccola (Northeastern University)
DTSTART:20220125T150000Z
DTEND:20220125T160000Z
DTSTAMP:20260423T004911Z
UID:TRAC/31
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/TRAC/31/">St
 ability of homological invariants of multiparameter persistence modules</a
 >\nby Luis Scoccola (Northeastern University) as part of The TRAC Seminar 
 - Théorie de Représentations et ses Applications et Connections\n\n\nAbs
 tract\nUnlike one-parameter persistence modules\, for which we have the ba
 rcode\, persistence modules with two or more parameters do not admit a com
 plete discrete invariant\, and thus incomplete invariants must be used to 
 study the structure of such modules in practice. The Hilbert function and 
 the multigraded Betti numbers are among the simplest such incomplete invar
 iants. Although these two invariants are already being used in application
 s\, it is a priori unclear whether they satisfy a stability result analogo
 us to the stability of the one-parameter barcode. Stability results are es
 sential for the interpretability and consistency of practical methods. I w
 ill present joint work with Steve Oudot in which we prove stability result
 s for multigraded Betti numbers and for the Hilbert function. I will also 
 discuss ongoing work in which we prove the stability of finer invariants c
 oming from different exact structures on a category of multiparameter pers
 istence modules.\n
LOCATION:https://researchseminars.org/talk/TRAC/31/
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