AOS · Asymptotics of Operator Semigroups

The theory of asymptotic behaviour of operator semigroups is a comparatively new field serving as a common denominator for many other areasof mathematics, such as for instance the theory of partial differential equations, complex analysis, harmonic analysis and topology.The primary interest in the study of asymptotic properties of strongly continuous operator semi-groups comes from the fact that such semigroupssolve abstract Cauchy problems which are often models for various phenomena arising in natural sciences, engineering and economics.Knowledge of the asymptotics of semigroups allows one to determine the character of long-time evolution of these phenomena.Despite an obvious importance, the asymptotic theory of one-parameter strongly continuous operator semigroups was for a very long time acollection of scattered facts rather than an organized area of research. The interest increased in the 1980s and the theory has witnessed adramatic development over the past thirty years.Still there is a number of notorious open problems that have been left open. These missing blocks prevent the theory from being complete, slowdown the development of the theory and discourage specialists from related fields to engage into the theory.The goal of the project is to give new impetus to the theory of asymptotic behavior of operator semigroups. To this aim we plan to extend andunify various aspects of the asymptotic theory of operator semigroups: stability, hyperbolicity, rigidity, boundedness, relations to Fredholmproperty, to work out new methods and to solve several long-standing open problems thus giving the theory its final shape.We intend to create an international forum that enables and promotes a multi- and cross- disciplinary exchange of ideas, methods and tools under the common umbrella of asymptotic theory of operator semigroups. Thus we expect that, moreover, a wide range of modern analysis will benefit from the project.