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UID:912f0ff9833df62fcd8972bbee4d5a66
CATEGORIES:Math and Data Seminar
CREATED:20250218T134319
SUMMARY:Inferring Dynamics with Generalized Persistence Diagrams
LOCATION:Hill 705
DESCRIPTION:Suppose we are given a sample of a discrete dynamical system φ: M → M. Can 
 we infer φ from this sample? Classical persistent homology can be used to a
 nalyze the sample and infer the homology of M. In this talk, we employ the 
 machinery of Persistent Local Systems (Patel and MacPherson) to not only re
 cover the persistent homology of the sample but also extract persistent inf
 ormation about the dynamics, all summarized in what we call the Generalized
  Persistence Diagram (Patel). Moreover, generalized persistence diagrams sa
 tisfy Bottleneck Stability, just like classical persistence. This implies t
 hat, under suitable assumptions on M and φ, the persistent dynamical inform
 ation is stable with respect to perturbations of the sample.\n
X-ALT-DESC;FMTTYPE=text/html:<p>Suppose we are given a sample of a discrete dynamical system φ: M → M. C
 an we infer φ from this sample? Classical persistent homology can be used t
 o analyze the sample and infer the homology of M. In this talk, we employ t
 he machinery of Persistent Local Systems (Patel and MacPherson) to not only
  recover the persistent homology of the sample but also extract persistent 
 information about the dynamics, all summarized in what we call the Generali
 zed Persistence Diagram (Patel). Moreover, generalized persistence diagrams
  satisfy Bottleneck Stability, just like classical persistence. This implie
 s that, under suitable assumptions on M and φ, the persistent dynamical inf
 ormation is stable with respect to perturbations of the sample.</p>
CONTACT:Amit Patel (Colorado State)
DTSTAMP:20260829T151613
DTSTART;TZID=America/New_York:20250314T150000
DTEND;TZID=America/New_York:20250314T160000
SEQUENCE:0
TRANSP:OPAQUE
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