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CATEGORIES:Junior Geometry Seminar
SUMMARY:The persistent homology of data - Nina Otter (Oxfo
rd)
DTSTART;TZID=Europe/London:20170512T150000
DTEND;TZID=Europe/London:20170512T160000
UID:TALK71326AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/71326
DESCRIPTION:Topological data analysis (TDA) is a field that li
es at the intersection of data analysis\, algebrai
c topology\, computational geometry\, computer sci
ence\, and statistics. The main goal of TDA is to
use ideas and results from geometry and topology t
o develop tools for studying qualitative features
of data. One of the most successful methods in TDA
is persistent homology (PH)\, a method that stems
from algebraic topology\, and has been used in a
variety of applications from different fields\, i
ncluding robotics\, materials science\, biology\,
and finance.\n\nPH allows to study qualitative fea
tures of data across different values of a paramet
er\, which one can think of as scales of resolutio
n\, and provides a summary of how long individual
features persist across the different scales of re
solution. In many applications\, data depend not o
nly on one\, but several parameters\, and to apply
PH to such data one therefore needs to study the
evolution of qualitative features across several p
arameters. While the theory of 1-parameter persist
ent homology is well understood\, the theory of mu
lti-parameter PH is hard\, and it presents one of
the biggest challenges of TDA.\n\nIn this talk I w
ill first give an introduction to persistent homol
ogy\; I will then discuss some applications\, and
the theoretical challenges in the multi-parameter
case. \n\nNo prior knowledge on the subject is ass
umed.\nThis talk is based on joint work with Heath
er Harrington\, Henry Schenck\, and Ulrike Tillman
n.
LOCATION:MR13
CONTACT:
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