Intersections of Schubert varieties and eigenvalue inequalities in an   arbitrary finite factor
  It is known that the eigenvalues of selfadjoint elements a,b,c with a+b+c=0 in the factor R^omega (ultrapower of the hyperfinite II1 factor) are characterized by a system of inequalities analogous to the classical Horn inequalities of linear algebra. We prove that these inequalities are in fact true for elements of an arbitrary finite factor. A matricial (`complete') form of this result is equivalent to an embedding question formulated by Connes. 
H. Bercovici, B. Collins, K. Dykema, W. S. Li, and D. Timotin