M/E23

Nemirovski asked in his plenary talk at ICM 2006 whether every convex semialgebraic set is a spectrahedral shadow, i.e. can be defined by linear matrix inequalities. Recently, Scheiderer answered this question to the negative by exhibiting first counter examples. In this talk I will present a joint work with Manuel Bodirsky and Andreas Thom in which we answer this question for certain sets that resisted the efforts of Scheiderer. Our approach relies on a simple model theoretic observation and differs from Scheiderer's methods substantially.

Mario Kummer

Dresden