Yohsuke Imagi

Last Update 2022/11/21
I am studying special Lagrangian geometry, an area of differential geometry. For YangMills instantons in dimension 4 and pseudoholomorphic 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 YangMills instantons in dimension 4, or those of pseudoholomorphic 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.
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