## Monday, 30 September 2019 Guest lectures: Martin R Bridson FRS, Maria J. Esteban and Volker Mehrmann

#### We are pleased to invite you to the following public lectures

on Tuesday, 8th of October 2019

at FAMNIT-VP1 (Glagoljaška 8, Koper)

### 11:15–12:00: *Hyperbolic geometry: where battered gems retain their full beauty*

Martin R Bridson FRS, 8ECM Prize Committee Chair

(University of Oxford)

__About the lecture:__

Hyperbolic geometry provides a rich setting in which many rigidity phenomena emerge. In this talk for a general audience, Martin R Bridson FRS shall present several different types of rigidity phenomena, from Mostow’s classical rigidity theorem to generalizations involving the large-scale geometry of groups and spaces. He shall also explain why hyperbolicity is so ubiquitous and end the lecture by sketching how a newly discovered rigidity phenomenon in hyperbolic geometry can be used to settle an old question concerning the difficulty of identifying an infinite group by studying its actions on finite objects.

### 12:00–12:45: *Best constants for functional inequalities and spectral estimates for Schrödinger operators*

Maria J. Esteban, 8ECM Scientific Committee Chair

(CEREMADE (CNRS UMR n° 7534), PSL Research University, Université Paris-Dauphine)

### 13:30–14.15: *The distance to stability and the distance to instability of dynamical systems*

Volker Mehrmann, President European Mathematical Society

(TU Berlin)

__About the lecture:__

The analysis of the stability of a dynamical system is an essential question of mathematics. An important class of control systems is that of dissipative Hamiltonian systems that arise in all areas of science and engineering. When the system is linearized arround a stationary solution one gets a linear dissipative Hamiltonian system. Despite the fact that the system looks very unstructured at firstsight, it has remarkable properties. Stability and passivity are automatic, Jordan structures forpurely imaginary eigenvalues, eigenvalues at infinity, and even singular blocks in the Kroneckercanonical form are very restricted and furthermore the structure leads to fast and efficientiterative solution methods for associated linear systems. We discuss the distance to instability under struture preserving perturbations and also the smallest distance to the nearest stable system. An even harder problem is the distance to the nearest singular or ill-posed problem. While this in gerenal open, for the class of dissipative Hamiltonian systems we present a simple classification.

This is joint work with Christian Mehl and Michal Wojtylak.