I-AIM Seminar Series with Kathryn Hess

November  20
Kathryn Hess, EPFL
“From Trees to Barcodes and Back Again“

Abstract: 
Methods of topological data analysis have been successfully applied in a wide range of fields to provide useful summaries of the structure of complex data sets in terms of topological descriptors, such as persistence diagrams. While there are many powerful techniques for computing topological descriptors, the inverse problem, i.e., recovering the input data from  topological descriptors, has proved to be challenging.
In this talk I will focus on the Topological Morphology Descriptor (TMD), which assigns a persistence diagram to any tree embedded in Euclidean space, and a sort of stochastic inverse to the TMD, the Topological Neuron Synthesis (TNS) algorithm. I will provide an overview of the TMD and the TNS and then describe the results of our theoretical and computational analysis of their behavior and properties, in which symmetric groups play a key role.  In particular, I will specify  the extent to which the TNS provides an inverse to the TMD.
This is joint work with Adélie Garin and Lida Kanari, based on earlier collaborations led by Lida.

About the Speaker:
Kathryn Hess is a professor of mathematics and life sciences at the EPFL.  She received her PhD from MIT and held positions at the universities of Stockholm, Nice, and Toronto before moving to the EPFL. Her research focuses on algebraic topology and its applications, primarily in the life sciences, but also in materials science. On the applied side, she has elaborated methods based on topological data analysis for high-throughput screening of nanoporous crystalline materials, classification and synthesis of neuron morphologies, and classification of neuronal network dynamics.  She has also developed and applied innovative topological approaches to network theory, leading to a powerful, parameter-free mathematical framework relating the activity of a neural network to its underlying structure, both locally and globally.
In 2016 she was elected to Swiss Academy of Engineering Sciences and was named a fellow of the American Mathematical Society and a distinguished speaker of the European Mathematical Society in 2017.