I am studying special Lagrangian geometry, an area of differential geometry. For Yang-Mills instantons in dimension 4 and pseudo-holomorphic curves, we already have a good understanding of singularities, and we can define a nice compactification of moduli spaces, which is a source of interesting mathematics and physics. One may want to do something similar for special Lagrangian submanifolds, but their singularities seem considerably more difficult to analyze than those of Yang-Mills instantons in dimension 4, or those of pseudo-holomorphic curves. So we have not yet achieved a“nice” compactification of the moduli space of special Lagrangian submanifolds. I am developing a deep theory on“simple”singularities, using some techniques from geometric measure theory and Lagrangian Floer theory.