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SUMMARY:Counting functions on the interval and the foundations of TDA
DTSTART:20170320T101500
DTEND:20170320T113000
DTSTAMP:20260510T131435Z
UID:75745c82e7deef5ee546b5b54f0601d3410c971fea4d49e630da6469
CATEGORIES:Conferences - Seminars
DESCRIPTION:Justin Curry (Duke)  \n\n \nTopology offers a set of descrip
 tors---trees\, persistence diagrams\, and sheaves---for the analysis of da
 ta where shape\, broadly speaking\, is important. I will present a new tec
 hnique called "chiral merge trees" especially suited to the study of time 
 series. Counting the number of chiral merge trees that realize a given per
 sistence diagram refines Arnold's Calculus of Snakes and has a suggestive 
 entropic interpretation. Since the space of trees is CAT(0)\, the existenc
 e of unique Fréchet means overcomes certain statistical challenges in per
 sistence. Finally\, I will discuss how constructible cosheaves provide a u
 nifying data structure for the study of multi-variate data\, where questio
 ns of numerical approximation and convergence are leading to the study of 
 analysis on these categorically defined structures.\n \n 
LOCATION:MA 31
STATUS:CONFIRMED
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