Horn Conjecture for finite von Neumann algebras

Series: 
Analysis Seminar
Monday, September 22, 2008 - 14:00
1 hour (actually 50 minutes)
Location: 
Skiles 255
,  
School of Mathematics, Georgia Tech
Organizer: 
The Horn inequalities give a characterization of eigenvalues of self-adjoint n by n matrices A, B, C with A+B+C=0. The proof requires powerful tools from algebraic geometry. In this talk I will talk about our recent result of these inequalities that are indeed valid for self-adjoint operators of an arbitrary finite factors. Since in this setting there is no readily available machinery from algebraic geometry, we are forced to look for an analysts friendly proof. A (complete) matricial form of our result is known to imply an affirmative answer to the Connes' embedding problem. Geometers in town especially welcome!