LMU



Münchner Mathematisches Kolloquium

Am Freitag, 01. Juli 2005, um 16 Uhr c.t. spricht

anlässlich des 125. Geburtstages von Oskar Perron

Prof. Roger Nussbaum, Ph. D.
(Rutgers University)

im Hörsaal E 27 über das Thema

Perron-Frobenius Theory and Games by the Seashore


Zusammenfassung: Almost one hundred years ago Perron and Frobenius developed a beautiful theory concerning eigenvalues and eigenvectors of nXn matrices A all of whose entries are nonnegative. If A is such a matrix and all the columns of a sum to one (so A is a column stochastic matrix), then for every nonnegative nX1 column vector x, there is a column vector y and an integer p such that A^kp(x) converges to y as k goes to infinity. Furthermore, p is the order of some element of the symmetric group on n letters.
Over the past twenty years, some remarkably precise analogues of the above result have been obtained for classes of nonlinear maps. Surprisingly, all of the basic difficulties are already apparent in a simple sand-shifting game which a mathematically inclined child might play by the seashore. We shall describe this sand-shifting game, give some theorems and discuss some open questions.

Alle Interessierten sind hiermit herzlich eingeladen. Eine halbe Stunde vor dem Vortrag gibt es Kaffee und Tee im Sozialraum (Raum 448) im 4. Stock.

Treffpunkt zum Abendessen um 19.00 Uhr wird noch bekannt gegeben.


Für die Mathematischen Fachbereiche der LMU und der TUM, die Dekane
Prof. Dr. H. Siedentop (LMU) und Prof. Dr. M. Brokate (TU).