  Background: low-mass stars are the dominant product of the star formation
process, and they trace star formation over the full range of environments,
from isolated globules to clusters in the central molecular zone. In the past
two decades, our understanding of the spatial distribution and properties of
young low-mass stars and protostars has been revolutionized by sensitive
space-based observations at X-ray and IR wavelengths. By surveying spatial
scales from clusters to molecular clouds, these data provide robust
measurements of key star formation properties.
  Goal: with their large numbers and their presence in diverse environments,
censuses of low mass stars and protostars can be used to measure the dependence
of star formation on environmental properties, such as the density and
temperature of the natal gas, strengths of the magnetic and radiation fields,
and the density of stars. Here we summarize how such censuses can answer three
basic questions: i.) how is the star formation rate influenced by environment,
ii.) does the IMF vary with environment, and iii.) how does the environment
shape the formation of bound clusters? Answering these questions is an
important step toward understanding star and cluster formation across the
extreme range of environments found in the Universe.
  Requirements: sensitivity and angular resolution improvements will allow us
to study the full range of environments found in the Milky Way. High spatial
dynamic range (< 1arcsec to > 1degree scales) imaging with space-based
telescopes at X-ray, mid-IR, and far-IR and ground-based facilities at near-IR
and sub-mm wavelengths are needed to identify and characterize young stars.
