  The Central Molecular Zone (CMZ; inner $\sim{}200~\rm{}pc$) of the Milky Way
is a star formation (SF) environment with very extreme physical properties.
Exploration of SF in this region is important because (i) this region allows us
to test models of star formation under exceptional conditions, and (ii) the CMZ
clouds might be suitable to serve as templates to understand the physics of
starburst galaxies in the nearby and the distant universe. For this reason we
launched the Galactic Center Molecular Cloud Survey (GCMS), the first
systematic study that resolves all major CMZ clouds at interferometer angular
resolution (i.e., a few arc seconds). Here we present initial results based on
observations with the Submillimeter Array (SMA) and the Atacama Pathfinder
Experiment (APEX). Our study is complemented by dust emission data from the
Herschel Space Telescope and a comprehensive literature survey of CMZ star
formation activity. Our research reveals (i) an unusually steep linewidth-size
relation, $\sigma(v)\propto{}r_{\rm{}eff}^{0.66\pm{}0.18}$, down to velocity
dispersions $\sim{}0.6~\rm{}km\,s^{-1}$ at 0.1 pc scale. This scaling law
potentially results from the decay of gas motions to transonic velocities in
strong shocks. The data also show that, relative to dense gas in the solar
neighborhood, (ii) star formation is suppressed by factors $\gtrsim{}10$ in
individual CMZ clouds. This observation encourages exploration of processes
that can suppress SF inside dense clouds for a significant period of time.
