SIAM Mini-Symposium : Sheaves and Homotopical Methods for Topological Data Analysis

Dear Applied Topologists,

It is our pleasure to invite you to the Mini-Symposium part of the SIAM-AG21 conference on Sheaves and Homotopical Methods for Topological Data Analysis, which will take place virtually on the 18th of August 2021.

If you are interested in participating, please register here before the 9th of August.

We look forward to see you there,

With best regards,

Nicolas Berkouk & François Petit

Abstract

The theory of one-parameter persistence was developed in the early 2000’s as an attempt to define topological descriptors of datasets which are robust to noise – the so-called barcodes. Since then, it has led to important advances in diverse areas: material sciences, time series analysis, neuroscience, and neural networks, just to name a few. Although well understood, one-parameter persistence faces several limitations such as sensitivity to outliers or to the user’s choice of the function filtering the data. To overcome these shortcomings, the persistence community has introduced a generalization of the above construction: multi-parameter persistence. In this context, the algebraic theory of multi-parameter persistence becomes more complex, and the need for more refined techniques originating from algebraic topology and algebraic geometry more evident. In this symposium, the speakers will present their advances in the field of topological data analysis with a sheaf theoretical or homotopical perspective. They will emphasize the benefits of taking a more abstract point of view on theoretical as well as on applied problems and explain the challenges of computability raised by these approaches.

Organizers: Nicolas Berkouk & François Petit

Program (Eastern Time)

9:00-9:25 Sheaves As Data Structures, abstract , Robert W. Ghrist, University of Pennsylvania, U.S.

9:30-9:55 Computational Topology in Intersection Theory, abstract, Vidit Nanda, University of Oxford, United Kingdom; Martin Helmer, University of California, Berkeley, U.S.

10:00-10:25 Distances on Sheaves, abstract, François Petit, Sorbonne Universités, France; François Petit, Université de Paris, France

10:30-10:55 The Amplitude of An Abelian Category: Measures in Persistence Theory, abstract, Nina Otter, University of California, Los Angeles, U.S.

2:40-3:05 Multi Parameter Persistence on Crossroads of Homotopy Theory and Statistics, abstract, Wojciech Chacholski, KTH Royal Institute of Technology, Sweden

3:10-3:35 Homotopy Invariant Notions of Interleaving and Applications, abstract, Luis Scoccola, Michigan State University, U.S.

3:40-4:05 Persistent Homotopical Algebra, abstract, Grégory Ginot, Université Paris 13, France

4:10-4:35 The Truncated Interleaving Distance for Reeb Graphs, abstract, Elizabeth Munch, Michigan State University, U.S.