Frechet differentiability of S^p norms

Abstract: 

One of the open questions in the theory of Schatten ideals S^p of compact operators is whether their norms have the same differentiability properties as the norms of their commutative counterparts.  The talk will answer the question positively.   The solution is based on earlier resolution of L.S. Koplienko’s conjecture concerning existence of higher order spectral shift functions.