Mathematics seminar - Thursday 28 April

[math]

M A T H E M A T I C S   S E M I N A R S   2011


Thursday, 28 April, at 15:00 hrs.


Professor Gautam Bharali
(Indian Institute of Science, Bangalore, India)


"Towards a sharp Schwarz Lemma for the spectral unit ball"


Abstract:

The spectral unit ball of dimension n^2 is the set of all n\times n 
matrices having spectral radius less than 1. This object is of some 
prominence in linear control-theory circles because the Pick-Nevanlinna 
interpolation problem on it is very challenging. A first step in solving 
this problem would be to solve the 2-point problem, i.e. to produce a 
Schwarz lemma for the spectral unit ball. This is hard because the 
spectral unit ball is non-homogeneous when n>1, but there have been some 
recent results which we shall discuss. The complex geometry of the 
spectral unit ball in n^2 (n>1) is interesting because GL(n,C) acts 
non-trivially on it by conjugation. We shall discuss how this feature 
points to the prospect of a sharp Schwarz lemma.



VENUE: Luigi Stasi Seminar Room
(ICTP Leonardo da Vinci Building, first floor)