ANALYSIS
SEMINAR

"The
Schur-Horn Theorem in Von Neumann Algebras"

by

Mohan Ravichandran

(Sabancı University)

Abstract: In 2002, Richard Kadison
published two delightful papers titled, ''The Pythagorean theorem,'' in which
he showed that thinking about the Pythagoras theorem leads one into very
interesting territory. The key point of his investigation is the so called
Carpenter's rule that says that if $a^{2} + b^{2} = c^{2}$, then there is a
right angled triangle with sides $a, b$ and $c$. In an entirely natural way, one
is led from the Carpenter's rule to asking for a characterization of diagonals
of projection matrices, something that follows from the celebrated Schur-Horn
theorem.

Kadison then formulated the problem of characterizing the diagonals
of projections in finite von Neumann algebras, but left the problem open. I was
able to give a complete solution to this problem, in part in joint work with
Rajarama Bhat of the Indian Statistical Institute. Our result is in fact much
more general - We are able to give a completely satisfactory Schur-Horn theorem
in von Neumann algebras, establishing a conjecture of Kadison and William
Arveson. I will report on this work and show how this problem is connected to
other problems in Hilbert spaces, including the famous Kadison-Singer problem
as well as frame theory.

Tea and cookies will be served after the
seminar.

Date:
Thursday, April 26, 2012

Time: 14.00 – 15:00

Place: Mathematics Seminar Room,
SA-141