Vorträge im Schwerpunkt Reelle Geometrie und Algebra
Donnerstag, 15. Juli 2010, um 17:00 Uhr
in F426
(Schwerpunktskolloquium)
Tim Netzer (Leipzig)
On the possibility and impossibility of determinantal representations of polynomials
Brändén has recently shown that there are real zero
polynomials without determinantal representations. This disproves the
generalized Lax conjecture, which was shown to be true in the case of
two variables by Helton and Vinnikov. One can easily improve
Brändéns result and show that there are very simple
explicit polynomials without determinantal representations, even of
degree two. On the other hand, these examples admit a determinantal
representation when raised to a high enough power. To prove this one
constructs an algebra with involution and shows that is has a finite
dimensional representation. The results are joint work with Andreas
Thom (work in progress).
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F 441 bei Tee und Kaffee zu treffen.
zuletzt
geändert am 12. Juli 2010
