I will discuss the characterization of convex sets in m
which can be represented by Linear Matrix Inequalities, i.e., as feasible
sets of semidefinite programmes. There is a simple necessary condition,
called rigid convexity, which has been shown to be sufficient for sets in
the plane and is conjectured to be sufficient (in a somewhat weakened
sense) for any m.
This should be contrasted with the situation for matrix convex sets that