21.11.2018 um 17:15 Uhr in 69/125:
Prof. Dr. Rob Eggermont (University of Technology Eindhoven)
Finitely Generated Spaces in High-Dimensional Settings with Symmetry
In a high-dimensional space with the Zariski topology, it is generally difficult to find equations generating a
given subspace. If the space has additional symmetries, the problem becomes easier, and it is sometimes
possible to use equations describing a smaller space in a lower-dimensional setting. As an example, to describe
matrices of rank at most 1 it suffices to know that any 2 by 2 determinant vanishes. This does not depend on
the size of the matrix. In this talk, we give some examples of high-dimensional settings with symmetry, and
describe more formally what we mean by finitely generated spaces in these settings. We will also talk about
some recent results.
28.11.2018 um 17:15 Uhr in 69/125:
Prof. Dr. Frank den Hollander (Universität Leiden)
Exploration on Dynamic Networks
Search algorithms on networks are important tools for the organisationof large data sets. A key example is Google PageRank, which assigns a numerical weight to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of measuring its relative importance within the set. The weighting is achieved by exploration.
The mixing time of a random walk on a random graph is the time it needs to approach its stationary distribution (also called equilibrium distribution). The characterisation of the mixing time has been the subject of intensive study. Many real-world networks are dynamic in nature. It is therefore natural to study random walks on dynamic random graphs.
In this talk we focus on a random graph with prescribed degrees. We investigate what happens to the mixing time of the random walk when at each unit of time a certain fraction of the edges is randomly rewired. We identify three regimes in the limit as the graph becomes large: fast, moderate, slow dynamics. These regimes exhibit surprising behaviour.
The talk is aimed at a general mathematics audience. No prior knowledge of probability theory or graph theory is required.