Conference Agenda

Overview and details of the sessions of this conference. Please select a date or location to show only sessions at that day or location. Please select a single session for detailed view (with abstracts and downloads if available).

 
Session Overview
Session
MS189, part 2: Geometry and topology in applications.
Time:
Friday, 12/Jul/2019:
3:00pm - 5:00pm

Location: Unitobler, F006
30 seats, 57m^2

Presentations
3:00pm - 5:00pm

Geometry and topology in applications.

Chair(s): Jacek Brodzki (University of Southampton, United Kingdom), Heather Harrington (University of Oxford)

This symppsium will bring together leading practitioners, mid-carreer scientists as well as PhD students and postdoctoral fellows who are interested in the theory and practice of the applications of geometry and topology in real life problems. The spectrum of possible applications is very wide, and covers the sciences, biology, medicine, materials science, and many others. The talks will address the theoretical foundations of the methodology as well as the state of the art of geometric and topological modelling.

 

(25 minutes for each presentation, including questions, followed by a 5-minute break; in case of x<4 talks, the first x slots are used unless indicated otherwise)

 

Persistent Betti numbers of random Cech complexes

Florian Pausinger
Queen's Univeristy Belfast

We study the persistent homology of random Cech 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 Cech 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.

This is joint work with Ulrich Bauer (TU Munich).

 

Topological Analyses of Time Series

Nikki Sanderson
Lawrence Berkeley National Laboratory

Measurements from real-world systems produce time series, or sequential scalar-valued data, that contain information about complicated higher dimensional dynamics of the underlying system. Extracting this information from time series is often done by frequency analyses and statistics which demand linearity and stationarity. We present topological methods for investigating dynamics from nonlinear, non-stationary time series in application to TMS-EEG data.

 

On the Robustness of the Homological Scaffold

Francesco Vaccarino
Politecnico di Torino

Abstract: Homological Scaffold has been firstly introduced by Petri, Expert, Vaccarino et al. in 2014 in studying the effects on the functional connectome of the human brain under the effect of psilocybin. At that time it was defined empirically by using javaplex. In this talk, we will present two new principled definitions of the scaffold and the results of a comparison of the three scaffolds on simulated and real data.

Joint work with A. De Gregorio, M.Guerra and G.Petri

 

Stable and discriminative topological invariants

Martina Scolamiero
KTH

In this talk I will describe a framework that allows to compute a new class of stable invariants for multi-parameter persistence. The key element of our approach is defining metrics induced by so called ‘noise systems’. Such metrics generalize the classical notion of interleaving distance. At the same time, in the one parameter case, they allow to overcome the usual dichotomy interpreting short bars in a barcode as noise and long bars as relevant information. I will then focus on one of the proposed invariants, the stable rank, address its statistical properties and show how we can improve classification by adapting the noise system to the task.