Felix Klein Colloquium: Evolutionen in der Analysis. Der erste Schritt setzt der Modellbildung ihre Grenzen

The quantitative modelling of natural processes has been an important field of application for differential equations since Newton. However, determinism in the tradition of Lagrange comes up against (at least) two systematic limits.

Firstly, the initial choice of mathematical means completely determines which conclusions are possible at all in the end - and which are not. This implies the risk that some natural phenomena are excluded from the subsequent mathematical model - for purely conceptual reasons.

Secondly, experience shows that not all details of the system are known. For example, physical parameters are often determined by measurement, and unexpected external influences can occur. Therefore, any continuous-time description is always associated with inaccuracies and uncertainties. However, the established methods using probabilities are sometimes not advisable - e.g. if (survival) risks are to be completely avoided.

These aspects lead to interesting questions in analysis. In this lecture, three outlined problem types serve as motivation to extend the common description of system states by vectors. (Partial) sets offer an interesting alternative that has been less popular so far. In doing so, we come up against numerous questions - for example: What changes with the step to sets instead of vectors? How should we then interpret an ordinary differential equation? Can such abstract systems be simulated? The colloquium will present the basic ideas of an approach and outline some of its perspectives.

Speaker: Prof. Dr. Thomas Lorenz, Universität Rostock

Time: 17:15 - 18:30 o'clock

Place: Building 48, room 210

The lectures of the Felix Klein Colloquium will be held at 17:15 in room 210 of the Mathematics Building 48. Beforehand - from 16:45 - there will be an opportunity to meet the speaker at the colloquium tea in room 580.