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 1: Geometry and topology in applications.
Time:
Thursday, 11/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)

 

Topological data analysis in materials science

Yasu Hiraoka
Kyoto University

Topological data analysis (TDA) is an emerging concept in applied mathematics in which we characterize “shape of data” using topological methods. In particular, the persistent homology and its persistence diagrams are nowadays applied to a wide variety of scientific and engineering problems. In my talk, I will explain our recent activity of TDA on materials science, e.g. glass, polymer, granular system, iron ore sinter etc. By developing several new mathematical tools based on quiver representations, inverse analysis, and machine learnings, we can explicitly characterize significant geometric and topological (hierarchical) features embedded in those materials, which are practically important for materials properties.

 

Optimal transport in tropical geometric phylogenetic tree space

Anthea Monod
Columbia University

Recent results by Monod et al. (2018) establish that palm tree space---that is, the space of phylogenetic trees in the tropical geometric construction, and endowed with the tropical metric---is a metric measure space with well-defined properties for probability and statistics on sets of phylogenetic trees. With the tropical metric as ground metric, we construct foundations for optimal transport theory on palm tree space. In particular, we build the Wasserstein-p metric which allows for the comparison of probability distributions of different random variables on palm tree space. We study the cases where p = 1, which gives an efficient way to compute geodesics, and p = 2, which gives deeper insight into the geometry of palm tree space.

This is joint work with Wuchen Li (UCLA) and Bo Lin (Georgia Tech).
 

Primary distance for multipersistence

Ezra Miller
Duke

When persistent homology is used to summarize data objects, distances between the resulting persistence modules serve as proxies for distances between the data objects themselves. In the presence of more than one parameter, module distances are complicated by the rich algebraic structure of multipersistence. In particular, unboundedness of the set of parameters presents problems with integration, interleaving, and other measures. Primary decomposition and algebraic operations related to it provide canonical (functorial) ways to extract bounded parameter sets, yielding convergence for existing measures that are based on integration. In addition, primary distances isolate from mixtures of multipersistence types pure contributions that would, in many existing measures, otherwise introduce bias when truncation or enforced decay are used without taking into account the algebraic structure.

 

Outlier robust subsampling techniques for persistent homology

Bernadette Stolz
Oxford

The amount and complexity of biological data has increased rapidly in recent years with the availability of improved biological tools. When applying persistent homology to large data sets, many of the currently available algorithms however fail due to computational complexity preventing many interesting biological applications. De Silva and Carlsson (2004) introduced the so called Witness Complex that reduces computational complexity by building simplicial complexes on a small subset of landmark points selected from the original data set. The landmark points are chosen from the data either at random or using the so called maxmin algorithm. These approaches are not ideal as the random selection tends to favour dense areas of the point cloud while the maxmin algorithm often selects outliers as landmarks. Both of these problems need to be addressed in order to make the method more applicable to biological data. We study new ways of selecting landmarks from a large data set that are robust to outliers. We further examine the effects of the different subselection methods on the persistent homology of the data.