Speaker: Yuriy Mileyko (UHM)
Title: Another look at recovering local homology from samples of stratified sets.
Recovering homological features of spaces from samples has become one of
the central themes in topological data analysis, which has led to many
successful applications. Most of the results in this area focus on
global homological features, whose recovery predicates on imposing well
understood geometric conditions on the underlying space. Existing work
on recovering local homological information of a space from samples has
been much less abundant, since the required local geometric conditions on
the underlying space may vary from point to point and are not easily
integrated into a global condition, unless the space is a smooth
manifold. In this talk, we show that such global conditions for
recovering local homological information can be obtained for a fairly
large class of stratified sets.