Robust control of linear partial differential equations
Lassi Paunonen (Tampere University of Technology)
In this presentation we discuss recent develoments and open problems in the theory of robust output tracking and disturbance rejection for linear infinite-dimensional systems. The presented theory can in particular be used in designing robust error feedback controllers for linear partial differential equations. The controllers solving the robust output tracking problem are characterized by the fundamental "Internal Model Principle" first presented for finite-dimensional systems in the 1970's. As our main results we present a generalization of the Internal Model Principle for infinite-dimensional linear systems. Finally, we discuss different internal model based controller structures for selected classes of linear partial differential equations.
Quasiconformal and quasisymmetric uniformization of metric spaces
Matthew Romney (University of Jyväskylä)
Which metric spaces can be parametrized by some Euclidean space under a quasiconformal or quasisymmetric mapping? We discuss some ongoing work in this area of research.
On the classification of nilpotent Lie groups up to quasi-isometry and Lie algebra cohomology
Thibaut Dumont (University of Jyväskylä)
In this GeoMeG meeting, I will survey the question of classifying (connected) simply connected nilpotent Lie groups up to quasi-isometry and present the known QI-invariants provided by Pansu, Shalom, and Sauer. Following Cornulier, these invariants are to be compared with the classification of nilpotent Lie algebras (hence of simply connected nilpotent Lie groups) up to dimension 7. The role of Lie algebra cohomology and the related spectral sequence will be discussed as they are the source of potential QI-invariants. If time permits or in a future meeting, we shall compare this to recent QI-rigidity results of Amann.
On the Entropy of Hilbert Geometries of Low regularities
Louis Merlin (Universite du Luxembourg)
The volume entropy of a metric measure space is the exponential growth rate of volumes of balls. A recent result of N. Tholozan shows that, in the context of Hilbert geometries, entropy can never exceed the hyperbolic entropy (n-1 in dimension n).
This result is absolutely not rigid and in fact, maximal entropy is achieved as soon as the boundary is sufficiently regular. This leads to the general question on the relation between the regularity of the convex set and the value of the volume entropy. The aim of this talk is to present two results which state that the relation does exist. This is a joint work with J. Cristina. In a first part of the talk, I'll carefully explain what are Hilbert geometries and try to give a feeling on the behavior of volume entropy in those spaces.