planned lectures for the SS 2018: **17.05.2018, 14.06.2018; 12.07.2018**

Past talks of the last semester can be found under **Veranstaltungen-Mathe**.

Donnerstag, 17. Mai 2018, 16:30 Uhr, Carl-Zeiß-Str. 3, SR 308

### Prof. Dr. Steffen Dereich (Westfälische Wilhelms-Universität Münster)

### Thema: A mathematical account on preferential attachment networks

**Abstract**: Since the 90s complex networks gained significant attention from different communities. One way mathematicians address complex networks is to define a sequence of random graphs with growing size and to ask for the behaviour of typical realizations when the network is large. A popular dynamic network model is the so called preferential attachment model where step by step new vertices are added and randomly connected with the earlier ones. This is done in such a way that links to vertices with high degree are preferred so that a fit-get-richer phenomenon can be observed. In this talk we discuss the typical structure of large networks with preferential attachment. We illustrate the artifacts caused by the dynamical building paradigm by comparing the result to static models. Further, we consider a variant of preferential attachment that shows a condensation phenomenon similar to certain physical models.

##### All interested parties are cordially invited!

Donnerstag, 14. Juni 2018, 16:30 Uhr, Carl-Zeiß-Str. 3, SR 308

### Prof. Dr. Michael Dellnitz (Universität Paderborn)

### Thema: Glimpse of the Infinite – on the Approximation of the Dynamical Behavior for Delay and Partial Differential Equations

**Abstract**: Over the last years so-called *set oriented *numerical methods have been developed for the analysis of the long-term behavior of finite-dimensional dynamical systems. The underlying idea is to approximate the corresponding objects of interest – for instance *global attractors *or related *invariant measures *– by box coverings which are created via multilevel subdivision techniques. That is, these techniques rely on partitions of the (finite-dimensional) state space, and it is not obvious how to extend them to the situation where the underlying dynamical system is infinite-dimensional.

In this talk we will present a novel numerical framework for the computation of finitedimensional dynamical objects for infinite-dimensional dynamical systems. Within this framework we will extend the classical set oriented numerical schemes mentioned above to the infinite-dimensional context. The underlying idea is to utilize appropriate *embedding techniques *for the reconstruction of global attractors in a certain finitedimensional space. We will also illustrate our approach by the computation of global attractors both for delay and for partial differential equations; e. g. the Mackey-Glass equation or the Kuramoto-Sivashinsky equation.

##### All interested parties are cordially invited!

Donnerstag, 12. Juli 2018, 16:30 Uhr, Carl-Zeiß-Str. 3, SR 308

### Prof. Dr. Werner Ballmann (Max-Planck-Institut Bonn)

### Thema: Small eigenvalues

**Abstract**: Eigenvalues of complete Riemannian manifolds are called small if they lie below the bottom of the spectrum of their respective universal covering spaces. For

example, eigenvalues of hyperbolic surfaces below a quarter are small. In the talk, I will discuss joint work with Henrik Matthiesen and Sugata Mondal on the number of small eigenvalues of Riemannian surfaces.

##### All interested parties are cordially invited!