Program here.

Seminar of applied mathematics will continue on October 1, 2pm in lecture room M5.

Julia Singer, Ph.D.

Walking through the statistical analysis plan of a clinical trial

Seminar of differential equations will continue on September 30, 2019 at 12pm in lecture room M5.

Univ.-Prof. Dr. Erika Hausenblas (Montanuniversität Leoben, Austria)

The Stochastic Gray Scott system

Abstract:

Reaction and diffusion of chemical species can produce a variety of patterns, reminiscent of those often seen in nature. The Gray Scott system is a coupled equation of reaction-diffusion type, modelling these kinds of patterns. Depending on the parameter, stripes, waves, cloud streets, or sand ripples may appear.

These systems are the macroscopic model of microscopic dynamics. Here, in the derivation of the equation, the random fluctuation of the molecules are neglected. Adding a stochastic noise, the inherent randomness of the microscopic behaviour is modelled. In particular, we add a time homogenous spatial Gaussian random field with a given spectral measure.

In the talk, we present our main result about the stochastic Gray Scott system. In addition, we introduce and explain an algorithm for its numerical approximation by an Operator splitting method. Finally, we present some examples illustrating the dynamical behaviour of the stochastic Gray Scott system.

We will continue on Thursday, October 3, in M5 at 1pm by the talk

P. Arndt

Ranges of functors and geometric elementary classes

Abstract:
Given first order theories S,T and a functor F:Mod(S)-->Mod(T) between their categories of models, one can ask whether objects in the image of F satisfy first order sentences other than those of T, or whether the essential image of F can be described as Mod(T') for an extension T' of T. If Mod(S), Mod(T) are k-accessible and F is a strongly k-accessible functor for some cardinal k, we can give criteria for this in the realm of Espíndola's k-geometric first order theories.
To this end we consider k-classifying toposes associated to S and T. The hypotheses ensure that the functor F is induced by a k-geometric essential morphism between them. The criteria are then obtained by factorizing this geometric morphism appropriately. We will explain the involved notions and give examples and applications.