Colloquium
University of Texas at Arlington - Department of Mathematics
Proudly Presents
Dr. Alejandro Uribe
Professor of Mathematics
University of Michigan
Friday, February 19, 2016
3:00 p.m.
311 Pickard Hall
“Spectral, pseudo-spectral, and numerical range asymptotics for
matrices and Schrödinger operators: An overview of old and new
results”
Abstract:
I will begin by a review of the concepts of spectrum, pseudospectrum and numerical range of
matrices, that is, in the context of linear algebra. Although these objects are closely related
for hermitian matrices, in the non-hermitian case they are remarkably different, which I will
illustrate with examples. I will then discuss asymptotic results of these objects, for certain
sequences of matrices (generalized Toeplitz matrices), and for certain Schrödinger operators
with complex potentials. I will end with a conjecture that is strongly supported by numerical
evidence, but that, to my knowledge, has not been settled.
Refreshments before the talk and socializing following the talk
http://www.uta.edu/math/pages/main/seminar.htm