Real algebra, random walks, and information theory
Tobias Fritz, Perimeter Institute
Similar to how commutative algebra studies rings and their ideals, the protagonists of real algebra are ordered rings. Their interplay between algebra and geometry is studied in terms of Positivstellen- stze, real analogs of the Nullstellensatz, which go back to Artin's solution of Hilbert's 17th problem. I will describe some of the state of the art in this eld, and then introduce a new Positivstellensatz which unies and generalizes several of the existing ones.