Dear All
Unfortunately Fred Chazal had to cancel his talk at the RSS meeting on Probability for Topological Data Analysis due to industrial action by French customs in Paris. The revised schedule for the meeting is as follows.
14:00--14:45 Florian Pausinger (Queen's University Belfast)
Title: Persistent Betti numbers of random Cech complexes
Abstract: We study the persistent homology of random \v{C}ech complexes. Generalizing a method of Penrose for studying random geometric graphs, we first describe an appropriate theoretical framework in which we can state and address our main questions. Then we define the k-th persistent Betti number of a random \v{C}ech complex and determine its asymptotic order in the subcritical regime. This extends a result of Kahle on the asymptotic order of the ordinary k-th Betti number of such complexes to the persistent setting.
Joint work with Ulrich Bauer (TU Munich).
14:45--15:30 Primoz Srkaba (Queen Mary University of London)
Title: Local-to-Global Stability Results for Persistence
Abstract: One of the main reasons for the popularity of persistence (and the corresponding invariant - a persistence diagram) is stability - under a certain class of perturbations, the difference output is well-behaved (can be bounded by the size of the perturbation of the input). The algebraically most natural metric for measuring the size of the perturbation is called the bottleneck distance. Unfortunately, this metric is a sup-norm, so proving convergence in statistical settings can be difficult. I will present the classical stability results as well as new results for Wasserstein distances. Finally I will discuss how local errors relate to global errors for persistence both for bottleneck and Wasserstein distances. No background in persistence will be assumed for the talk.
15:30--16:00 Break
16:00--17:30 Open problem and brainstorming session
There is a plan to have dinner at Baracca after the meeting.
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