Alladi Ramakrishnan Hall

The Kadison-Singer problem (1959-2013)

Mohan Ravichandran

Minar-Sinan Fine Arts University

In this first talk, I'll introduce the
Kadison-Singer problem (solved in 2013 by Adam Marcus, Daniel Spielman
and Nikhil Srivastava) and the related but weaker Restricted
invertibility principle. I will talk about techniques from geometric
functional analysis that can be applied to these, culminating in the
work of Joel Tropp who gave the best results prior to the work of
Spielman and Srivastava using fundamental techniques including Pietsch
Factorization and the little Grothendieck inequality. I will also
describe applications of these results to geometric functional
analysis and convex geometry.

Spielman and Srivastava would introduce a completely different method
of approaching these problems in 2011 that would be further developed
by them together with Adam Marcus to lead to a solution of the
Kadison-Singer problem in 2013. These new techniques will be the
subject of the next talk.