[CvGmt News] [Notiziario] [Settimanale] avviso seminario prof. Michael Overton (25.06.2019)

[Valeria Giuliani]

SEMINARIO DI MATEMATICA



*Martedì 25 giugno 2019*

ore 11:00



*Scuola Normale Superiore*

Pisa

Aula Mancini



*Michael Overton*
(New York University)



Terrà un seminario dal titolo:



*“**Crouzeix’s conjecture**”*





*Abstract:*

Crouzeix's conjecture is among the most intriguing developments in matrix
theory in recent years. Made in 2004 by Michel Crouzeix, it postulates
that, for any polynomial p and any matrix A, ||p(A)|| <= 2 max(|p(z)|: z in
W(A)), where the norm is the 2-norm and W(A) is the field of values
(numerical range) of A, that is the set of points attained by v*Av for some
vector v of unit length.  Crouzeix proved in 2007 that the inequality
above  holds if 2 is replaced by 11.08, and recently this was greatly
improved by Palencia, replacing 2 by 1+sqrt(2).  Furthermore, it is known
that the conjecture holds in a number of special cases, including n=2.  We
use nonsmooth optimization to investigate the conjecture numerically by
locally minimizing the “Crouzeix ratio”, defined as the quotient with
numerator the right-hand side and denominator the left-hand side of the
conjectured inequality. We also present local nonsmooth variational
analysis of the Crouzeix ratio at conjectured global minimizers.  All our
results strongly support the truth of Crouzeix’s conjecture.





Tutti gli interessati sono invitati a partecipare.



Classe di Scienze


Valeria Giuliani
Scuola Normale Superiore
Servizio alla Didattica e Allievi
tel. 050 509260
Piazza dei Cavalieri, 7
56126 Pisa
E-mail: valeria.giuliani at sns.it
E-mail: classi at sns.it

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