One problem of concern is that of the solvability of partial differential equations. Should we develop a method to determine if, and where, a given equation is solvable many problem so f mathematical physics will be settled.
Here is a description of work we are doing in the investigation of partial differential operators on the Heisenber group, a well established structure.
Here is a talk given by Chris Winfield at the AMS Meeting in New Orleans, 2011.
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