  Topological Data Analysis (TDA) is a field that leverages tools and ideas
from algebraic topology to provide robust methods for analysing geometric and
topological aspects of data. One of the principal tools of TDA, persistent
homology, produces a quantitative description of how the connectivity and
structure of data changes when viewed over a sequence of scales. We propose
that this presents a means to directly probe topological objects in gauge
theories. We present recent work on using persistent homology to detect center
vortices in SU(2) lattice gauge theory configurations in a gauge-invariant
manner. We introduce the basics of persistence, describe our construction, and
demonstrate that the result is sensitive to vortices. Moreover we discuss how,
with simple machine learning, one can use the resulting persistence to
quantitatively analyse the deconfinement transition via finite-size scaling,
providing evidence on the role of vortices in relation to confinement in
Yang-Mills theories.
