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SUMMARY:The persistent homology of data - Nina Otter (Oxford)
DTSTART:20170512T140000Z
DTEND:20170512T150000Z
UID:TALK71326@talks.cam.ac.uk
CONTACT:36916
DESCRIPTION:Topological data analysis (TDA) is a field that lies at the in
 tersection of data analysis\, algebraic topology\, computational geometry\
 , computer science\, and statistics. The main goal of TDA is to use ideas 
 and results from geometry and topology to develop tools for studying quali
 tative features of data. One of the most successful methods in TDA is pers
 istent homology (PH)\, a method that stems from algebraic topology\, and h
 as been used in a variety of applications from different  fields\, includi
 ng robotics\, materials science\, biology\, and finance.\n\nPH allows to s
 tudy qualitative features of data across different values of a parameter\,
  which one can think of as scales of resolution\, and provides a summary o
 f how long individual features persist across the different scales of reso
 lution. In many applications\, data depend not only on one\, but several p
 arameters\, and to apply PH to such data one therefore needs to study the 
 evolution of qualitative features across several parameters. While the the
 ory of 1-parameter persistent homology is well understood\, the theory of 
 multi-parameter PH is hard\, and it presents one of the biggest challenges
  of TDA.\n\nIn this talk I will first give an introduction to persistent h
 omology\; I will then discuss some applications\, and the theoretical chal
 lenges in the multi-parameter case. \n\nNo prior knowledge on the subject 
 is assumed.\nThis talk is based on joint work with Heather Harrington\, He
 nry Schenck\, and Ulrike Tillmann.
LOCATION:MR13
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