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We present a large-scale survey of the central molecular zone (CMZ) of our Galaxy, as well as a monitoring program of Sgr A*, with the AzTEC/Large Millimeter Telescope (LMT) in the 1.1 mm continuum. Our 1.1 mm map covers the main body of the CMZ over a field of $1.6 \times 1.1$ deg$^2$ with an angular resolution of $10.5''$ and a depth of 15 mJy/beam. To account for the intensity loss due to the background removal process, we combine this map with lower resolution CSO/Bolocam and \textit{Planck}/HFI data to produce an effective full intensity 1.1 mm continuum map. With this map and existing \textit{Herschel} surveys, we have carried out a comprehensive analysis of the spectral energy distribution (SED) of dust in the CMZ. A key component of this analysis is the implementation of a model-based deconvolution approach, incorporating the Point Spread Functions (PSFs) of the different instruments, and hence recovering a significant amount of spatial information on angular scales larger than $10.5''$. The monitoring of Sgr A* was carried out as part of a worldwide, multi-wavelength campaign when the so-called G2 object was undergoing the pericenter passage around the massive black hole (MBH). Our preliminary results include 1) high-resolution maps of column density, temperature and dust spectral index across the CMZ; 2) a 1.1~mm light curve of Sgr A* showing an outburst of $140\%$ maximum amplitude on 9th May, 2014 but otherwise only stochastic variations of $10\%$ and no systematic long-term change, consistent with other observations.