Nonlinear Perron-Frobenius Theory

For Bas Lemmens a mathematician is

Somebody who explores some relevant abstract structures.

We are delighted to officially announce the commencement of the new RGOSA seminar season. We are thrilled to start this year’s series with a distinguished guest, Pr. Bas Lemmens.

The seminars are scheduled to take place every Thursday at 2:00 PM Tunis time (Tunisia). Your participation and engagement are highly encouraged as we embark on this enlightening journey of knowledge sharing.

The link for the seminar is below:

This Thursday, September 7, 2023 and the following Thursday, Pr. Bas Lemmens will talk about:

Nonlinear Perron-Frobenius Theory

The abstract of his talks is: 

Sometimes in mathematics a simple-looking observation opens up a new road to a fertile field. Such an observation was made independently by Garrett Birkhoff and Hans Samelson, who remarked that one can use Hilbert’s (projective) metric and the contraction mapping principle to prove some of the theorems of Perron and Frobenius concerning eigenvectors and eigenvalues of nonnegative matrices. This idea has been pivotal for the development of nonlinear Perron–Frobenius theory.
In the past few decades a number of strikingly detailed nonlinear extensions of Perron–Frobenius theory have been obtained. These results provide an extensive analysis of the eigenvectors and eigenvalues of various classes of order-preserving (monotone) nonlinear maps and give information about their iterative behavior and periodic orbits. They have found applications in computer science, mathematical biology, game theory and the study of dynamical systems.  

This two-part lecture provides an introduction to nonlinear Perron-Frobenius theory.

Posted in Seminar 2023 - 2024.