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15.10.2018 16:15 Katie Fitch (TUM):
A new method for directed graph symmetrizationMI 03.06.011 (Boltzmannstr. 3, 85748 Garching)

In this talk I will present a new method for symmetrization of directed graphs that arises from the studying the steady state dynamics of a network under a simple noisy consensus process. The symmetrization method constructs an undirected graph with equivalent pairwise effective resistances as a given directed graph. Consequently a graph metric, square root of effective resistance, is preserved between the directed graph and its symmetrized version. I will show that the preservation of this metric allows for interpretation of algebraic and spectral properties of the symmetrized graph in the context of the directed graph, due to the relationship between effective resistance and the Laplacian spectrum. Additionally, I will demonstrate a decomposition procedure for directed graph Laplacian matrices and conclude with relevant applications.

15.10.2018 16:30 Benedikt Stufler (University of Zurich) :
Invariance principles for random planar structures2.01.10 (Parkring 11, 85748 Garching-Hochbrück)

Invariance principles provide a universal description of the behaviour of a general class of random objects. For example, if a random walk lies in the domain of attraction of a stable law, then it converges after an appropriate rescaling to the corresponding stable Lévy process. The past decades have seen rapidly growing research activity on related universal limit objects for random planar structures, such as trees or graphs embedded on a fixed surface. The talk is meant to give an introduction to this topic, outline some selected results, and discuss future research directions.

17.10.2018 16:00 Prof. Claudia Redenbach (TU Kaiserslautern):
Anisotropy analysis of spatial point patternsMI HS 3 (Boltzmannstr. 3, 85748 Garching)

This talk will give an overview of techniques for detecting anisotropy in spatial point patterns. As an example of application, we will analyse the pore system in polar ice. In a depth below approx. 100 m, the ice contains isolated air bubbles which can be studied by using tomographic images of ice core samples. Interpreting the system of bubble centres as a realisation of a regular point process subject to geometric anisotropy, preferred directions and strength of compression can be estimated.

22.10.2018 15:30 Tal Orenshtein:
Ballistic RWRE as rough paths - convergence and area anomaly 2.01.10 (Parkring 11, 85748 Garching-Hochbrück)

We shall discuss our work on ballistic RWRE. We show that the annealed functional CLT holds in the rough path topology, which is stronger than the uniform one. This yields an interesting phenomenon: the scaling limit of the area process is not solely the Levy area, but there is also an additive linear correction which is called the area anomaly when is non-zero. Moreover, the latter is identified in terms of the walk on a regeneration interval and the asymptotic speed. A general motivation for achieving limit theorems for discrete processes in the rough path topology is the following property, which might be useful e.g., for simulations. Consider a nice difference equation driven by the recentered walk. A result by D. Kelly gives a scaling limit to the corresponding SDE, with an appropriate correction expressed explicitly in terms of the area anomaly. This is a joint work in progress with Olga Lopusanschi (Paris-Sorbonne)

22.10.2018 16:15 Alexandra Neamtu (TUM):
A rough introduction to rough paths theory with applications to SPDEsMI 03.06.011 (Boltzmannstr. 3, 85748 Garching)

We present a concise pathwise construction of stochastic integrals with respect to -Hölder continuous processes. This allows us to investigate the well-posedness of stochastic evolution equations driven by multiplicative rough noise such as the fractional Brownian motion. Moreover, this pathwise approach provides an appropriate setting for the analysis of the long-time behavior for this kind of SPDEs. This talk is based on a joint work with Robert Hesse.

22.10.2018 16:30 Timo Hirscher (Stockholm University) :
The Schelling model for segregation on Z2.01.10 (Parkring 11, 85748 Garching-Hochbrück)

Abstract: In 1969, economist T. Schelling invented a simple model of interacting particles to explain racial segregation in American cities: The nodes of a simple graph are occupied by agents of different kinds and each of them is inclined to have neighbors of its own kind. While Schelling used pennies and dimes on a checkerboard to implement some old-school-simulations on a finite instance, we are interested in the corresponding model on Z, the one-dimensional integer lattice. It turns out that the asymptotics are similar to the one of the voter model - but only if the range of a move is unbounded.

23.10.2018 16:30 Eugene Bogomolny (Paris, France)):
tbaMI 03.10.011 (Boltzmannstr. 3, 85748 Garching)


29.10.2018 16:15 Tobias Hurth (EPFL, Schweiz):
Random switching between deterministic vector fieldsMI 03.06.011 (Boltzmannstr. 3, 85748 Garching)

We consider a class of random dynamical systems characterized by Poissonian switching between deterministic vector fields on a finite-dimensional smooth manifold. If we record both the position of the switching trajectory on the manifold and the current driving vector field, we obtain a two-component Markov process. In this talk, we will discuss sufficient conditions for exponential convergence in total variation to the invariant measure of the associated Markov semigroup, and illustrate these conditions through several examples. The talk is based on work with Michel Benaïm and Edouard Strickler.

30.10.2018 17:00 Phillip Schroeder (Uni Göttingen):
High-order pressure-robust FEM and the importance of incompressible generalised Beltrami flowsGebäude 33, Raum 1431 (Werner-Heisenberg-Weg 39, 85577 Neubiberg)

The ability of a numerical method to preserve large-scale/coherent structures of a flow is fundamentally important in computational fluid dynamics. In this talk, we consider this phenomenon and compare numerical results for different Discontinuous Galerkin (DG) methods. The strong differences are then linked to the concept of pressure-robustness by means of a discrete Helmholtz projection and the resulting decomposition. It turns out that strong gradient forces in the convective term are present in many important flows. This observation is used to introduce the large class of incompressible generalised Beltrami flows. The remainder of the talk addresses when and why pressure-robust FEM can be superior (both in terms of efficiency and accuracy) and the role of high-order discretisations is discussed.