# Speakers

We are happy to feature the following awesome speakers (this list is expanded on a rolling basis, stay tuned for more!):

- Andrew J. Blumberg
- Peter Bubenik
- Gunnar Carlsson
- Mathieu Carrière
- Chao Chen
- Lorin Crawford
- Brittany Terese Fasy
- Robert Ghrist
- Kathryn Hess
- Yasu Hiraoka
- Leland McInnes
- Facundo Mémoli
- Liz Munch
- Vidit Nanda
- Jose Perea
- Raúl Rabadán
- Katharine Turner
- Bei Wang
- Yusu Wang
- Yuzuru Yamakage

**Keynotes** will be given by:

## Andrew J. Blumberg

Affiliation |
University of Texas at Austin |

## Peter Bubenik

Affiliation |
University of Florida |

## Gunnar Carlsson

Affiliation |
Stanford University |

## Mathieu Carrière

Affiliation |
Columbia University |

## Chao Chen

Affiliation |
Stony Brook University |

## Lorin Crawford

A Machine Learning Pipeline for Feature Selection and Association Mapping with 3D Shapes |

It has been a long-standing challenge to implement an analogue of variable selection with 3D shapes as the covariates in a regression model. Here, we present SINATRA, a statistical pipeline for sub-image selection where the goal is to identify the physical features of 3D shapes that best explain the variation between two trait classes. A key insight is that, one can use tools from differential topology to transform objects represented as meshes into a collection of vectors (with little to no loss of information about their natural structure). Since this topological transformation is invertible, SINATRA uses an interpretable machine learning algorithm to map significant vector indices back onto the original shapes — thus, highlighting the physical 3D shape characteristics that best distinguish members in the two groups. As an application of our pipeline, we conduct feature selection on a dataset consisting of mandibular molars from five different genera of New World Monkeys and examine the physical properties of their teeth that best characterize their dietary regimens. |

Affiliation |
Microsoft Research & Brown University |

Twitter |
@lorin_crawford |

Biography |
Lorin Crawford is a Senior Researcher at Microsoft Research New England. He also holds a position as the RGSS Assistant Professor of Biostatistics at Brown University. His scientific research interests involve the development of novel and efficient computational methodologies to address complex problems in statistical genetics, cancer pharmacology, and radiomics (e.g., cancer imaging). Dr. Crawford has an extensive background in modeling massive data sets of high-throughput molecular information as it pertains to functional genomics and cellular-based biological processes. His most recent work has earned him a place on Forbes 30 Under 30 list, The Root 100 Most Influential African Americans list, and recognition as an Alfred P. Sloan Research Fellow. |

## Brittany Terese Fasy

Searching in the Space of Persistence Diagrams |

The doubling dimension of the space of persistence diagrams is infinite and, as a result, current approaches for finding the nearest neighbor to a persistence diagram among a set of other persistence diagrams is either linear in the number of diagrams or does not offer performance guarantees. This talk will present the first algorithm that supports approximate nearest neighbor search in the space of persistence diagrams using the bottleneck distance. |

Affiliation |
Montana State University |

Twitter |
@topologybee |

Biography |
Brittany Terese Fasy is an assistant professor at Montana State University. She earned her PhD from Duke University in 2012. Her research is in computational topology. She studies topological descriptors (such as the persistence diagram) from both theoretical and applied perspectives. In addition, she studies data on graphs, directed topological spaces, and algorithmic problems in computational topology. Her research is grounded in real-world applications, including road network analysis and prostate cancer prognosis. |

## Robert Ghrist

Affiliation |
University of Pennsylvania |

Twitter |
@robertghrist |

Biography |
Robert Ghrist is the Andrea Mitchell PIK Professor of Mathematics and Electrical & Systems Engineering at the University of Pennsylvania. After earning a BS in Mechanical Engineering (University of Toledo, 1991), and the MS and PhD in Applied Mathematics (Cornell University, 1994, 1995), he held positions in Mathematics departments at the University of Texas (Austin), Georgia Tech, and the University of Illinois (Urbana-Champaign). He has been at Penn since 2008. Ghrist is a recognized leader in the field of Applied Algebraic Topology, with publications detailing topological methods for sensor networks, robotics, signal processing, data analysis, optimization, and more. He is the author of a leading textbook on the subject (Elementary Applied Topology, 2014), and has managed numerous large DoD grants from AFOSR, ASDRE, DARPA, and ONR. His research has been recognized with the NSF CAREER, NSF PECASE, SciAm50, and Vannevar Bush Faculty Fellow awards. Ghrist has been an invited speaker at two International Congresses of Mathematicians: once (Madrid 2006) for research and once (Seoul, 2014) for education. Ghrist is a dedicated expositor and communicator of Mathematics, with teaching awards that include the MAA James Crawford Prize, Penn’s Lindback Award, and the S. Reid Warren award in Engineering at Penn. Ghrist is the author, designer, and animator of popular YouTube video texts (featuring the Calculus BLUE Project), as well as an online course on Coursera featured in the New York Times, BoingBoing, and Gizmodo. |

## Kathryn Hess

Topological insights in neuroscience |

I will describe two applications of TDA in neuroscience that provide intriguing insights into the relation between between structure and function in networks of neurons. |

Affiliation |
École polytechnique fédérale de Lausanne (EPFL) |

Biography |
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. |

## Yasu Hiraoka

Characterizing rare events in persistent homology |

Indecomposables obtained through decompositions of persistent homology are regarded as topological summary of real data. However, as is well known, there exist pathologically complicated indecomposables in multi-parameter persistent homology in purely algebraic setting, and this fact makes it difficult to build mathematical theory on that setting. Our fundamental question is, how much should we care about such complicated indecomposables in the real data, and what is a suitable framework to study this question? To this aim, we will show several ongoing results, especially, (1) large deviation principle on 1 parameter persistent homology, and (2) law of large numbers on multi-parameter persistent homology. Then we will discuss how these two results (partially) answer to the original question. |

Affiliation |
Kyoto University |

Biography |
Yasu Hiraoka is a professor of Kyoto University Institute for the Advanced Study (KUIAS) at Kyoto University. He studies mathematical theory and algorithm of TDA, and also works on applying them into scientific and engineering problems. His primary interest is to develop descriptors for characterizing shape of complex and big data. By combining various mathematical theories such as topology, representation theory, probability theory, he succeeded in making TDA powerful and general for practical problems. In applications, he has organized the materials TDA team, and his group achieved several pioneering results on structural analysis in materials science based on TDA. In particular, a series of methods developed by his group using persistent homology, machine learning, and inverse analysis are expected to be a key technology for materials informatics in future. In addition to materials science, he has recently launched TDA projects on other application areas such as life science and economics. |

## Leland McInnes

UMAP + MAPPER = UMAPPER |

Combining UMAP and MAPPER to provide richer representations of naturally filtered datasets. |

Affiliation |
Tutte Institute for Mathematics and Computing |

Twitter |
@leland_mcinnes |

Biography |
Leland McInnes is a researcher at the Tutte Institute for Mathematics and Computing working on topologically motivated methods in data science. He balances his time between theoretical research, software engineering and implementation, and domain specific problems. |

## Facundo Mémoli

Spatiotemporal Persistent Homology for Dynamic Metric Spaces |

Characterizing the dynamics of time-evolving data within the framework of topological data analysis (TDA) has been attracting increasingly more attention. Popular instances of time-evolving data include flocking/swarming behaviors in animals and social networks in the human sphere. A natural mathematical model for such collective behaviors is a dynamic point cloud, or more generally a dynamic metric space (DMS). We show how to extend the Rips filtration stability result for (static) metric spaces to the setting of DMSs, while retaining stability. We identify polynomial time computable invariants and associated pseudodistances, and provide software implementations which can be used for practical tasks. This is joint work with Woojin Kim (Duke) and Nate Clause (OSU); see https://github.com/ndag/PHoDMSs. |

Affiliation |
Ohio State University |

Biography |
Facundo Mémoli is a professor in the Department of Mathematics and in the Department of Computer Science and Engineering at the Ohio State University. his research interests include topics in the intersection of metric geometry, topology, optimal transport, and applications to science and engineering such as topological data analysis, and networks. |

## Liz Munch

Persistent homology of complex networks for dynamic state detection in time series |

There has been extensive work performing time series analysis with persistence diagrams via the Takens embedding. In this talk we develop an alternative approach for studying graph representations of time series of dynamical systems. Specifically, we show how persistent homology can be used to yield a compressed, multi-scale representation of the ordinal partition network of the time series that can distinguish between dynamic states such as periodic and chaotic behavior. By replacing the network with its persistence diagram, we then extract existing as well as new geometric and entropy point summaries from the persistence diagram and compare to other commonly used network characteristics. Our results show that persistence-based point summaries yield a clearer distinction of the dynamic behavior and are more robust to noise than existing graph-based scores, especially when combined with ordinal graphs. |

Affiliation |
Michigan State University |

Twitter |
@elizabethmunch |

Biography |
Liz received her PhD from the Department of Mathematics at Duke University in May 2013. Prior to joining the faculty of Michigan State University, she was an Assistant Professor in the Department of Mathematics and Statistics at the University at Albany - SUNY, and a Postdoctoral Fellow at the Institute for Mathematics and its Applications at the University of Minnesota for the 2013-2014 thematic year on applications of topology. She also holds a Master of Arts in Mathematics from Duke University, a Bachelor of Science in Mathematics from the University of Rochester, and a Bachelor of Music in Harp Performance from the Eastman School of Music. When she isn’t thinking about TDA, she’s chasing her two sons around, playing video games, or watching bad sci-fi. |

## Vidit Nanda

Singularity detection in data |

I will describe a new and efficient topological technique to detect manifold-intersections and other singularities directly from finite point samples. The method makes use of local persistent homology computations around tiny annular neighborhoods of sampled data points, and works even when none of those points have been sampled from the singular regions. All of this is joint work with B Stolz, H Harrington and J Tanner. |

Affiliation |
University of Oxford |

Twitter |
@viditnanda |

Biography |
Vidit Nanda is an Associate Professor of Mathematics at Oxford, working broadly in the field of applied algebraic topology. Before coming to Oxford, he held postdoctoral positions at the Institute for Advanced Study, the Alan Turing Institute, and the University of Pennsylvania. |

## Jose Perea

TALLEM – Topological Assembly of LocalLy Euclidean Models |

We present here a new unsupervised topological data analysis tool for data coordinatization, fusion and distributed nonlinear dimensionality reduction. This new methodology, called TALLEM, assembles a collection of local Euclidean coordinates on the data, and leverages ideas from the theory of fiber bundles to yield a global map consistent with the underlying data topology. |

Affiliation |
Michigan State University |

Biography |
I got my Ph.D. in Mathematics from Stanford University in 2011, and a B.Sc. in Mathematics from Universidad del Valle (Summa cum laude and Valedictorian) in 2006. I was a postdoc in the department of Mathematics at Duke from 2011 to 2015, and a member of the Institute for Mathematics and its Applications (IMA) at the University of Minnesota during the Fall of 2014. In August of 2015 I joined Michigan State University as an Assistant Professor with joint appointments in the department of Computational Mathematics, Science & Engineering (CMSE), and the department of Mathematics. My work has been supported by grants from DARPA, the National Science Foundation, the Center for Business and Social Analytics, and an NSF CAREER award. |

## Raúl Rabadán

Affiliation |
Columbia University |

Biography |
Raul Rabadan is the Gerald and Janet Carrus Professor in the Departments of Systems Biology, Biomedical Informatics and Surgery at Columbia University. He is the director of the Program for Mathematical Genomics at Columbia University and the NCI Center for Topology of Cancer Evolution and Heterogeneity. From 2001 to 2003, Dr. Rabadan was a fellow at the Theoretical Physics Division at CERN, the European Organization for Nuclear Research, in Geneva, Switzerland. In 2003 he joined the Physics Group of the School of Natural Sciences at the Institute for Advanced Study. Previously, Dr. Rabadan was the Martin A. and Helen Chooljian Member at The Simons Center for Systems Biology at the Institute for Advanced Study in Princeton, New Jersey. He has been named one of Popular Science’s Brilliant 10 (2010), a Stewart Trust Fellow (2013), and he received the Harold and Golden Lamport Award at Columbia University (2014) and the Diz Pintado award (2018). Dr. Rabadan’s current interest focuses on uncovering patterns of evolution in biological systems through the lens of genomics. His recent interests include the development of mathematical approaches to uncover the evolution of cancer and infectious diseases, including topological data analysis and Random Matrix Theory, among others. |

## Katharine Turner

Affiliation |
Australian National University |

Biography |
Katharine Turner was an undergraduate at the University of Sydney and then did her PhD with Shmuel Weinberger at the University of Chicago (2015). After a postdoc at EPFL working with both Kathryn Hess and Victor Panaretos, she returned back down under and joined the Mathematical Sciences Institute at the Australian National University from 2017 as a Lecturer. In 2020 she was awarded an Discovery Early Career Research Award by the Australian Research Council. |

Wasserstein Stability for Persistence Diagrams |

The stability of persistence diagrams is among the most important results in applied and computational topology but most results are with respect to the bottleneck distance between diagrams. This has two main implications: it makes the space of persistence diagrams rather pathological and it is often provides very pessimistic bounds with respect to outliers. In this talk I will discuss new stability results with respect to the p-Wasserstein distance between persistence diagrams. The foundations are cellular stability functions on sufficiently finite spaces in terms of the p-norm of the perturbations. This has applications to image analysis, persistence homology transforms and Vietoris-Rips complexes. This is joint work with Primoz Skraba. |

## Bei Wang

Topology and Neuron Activations in Deep Learning |

Deep convolutional neural networks have become ubiquitous in image classification tasks thanks to architectures such as GoogLeNet and ResNet. However, we do not quite understand how these networks achieve their impressive performance. The main challenge in deep learning is the interpretability: How can we make the representations learned by these networks human interpretable? Given a trained deep neural network, we can address the interpretability issue by probing neuron activations, that is, the combinations of neuron firings, in response to a particular input image. With millions of input images, we can obtain a global view of what the neurons have learned by studying neuron activations at a particular layer and across multiple layers. We aim to shed light on the following questions using topological tools: What is the shape of the activation space? What is the organizational principle behind neuron activations? |

Affiliation |
University of Utah |

Twitter |
@beiphillips |

Biography |
Bei Wang is an assistant professor at the School of Computing and a faculty member in the Scientific Computing and Imaging (SCI) Institute, University of Utah. She received her Ph.D. in Computer Science from Duke University. Her research interests include topological data analysis, data visualization, computational topology, machine learning, and data mining. Her work spans both theoretical and applied research. Some of her recent research activities draw inspirations from topology, geometry, and machine learning, in studying brain networks, vector fields, tensor fields, and high-dimensional point clouds that arise from scientific simulations. |

## Yusu Wang

Affiliation |
University of California, San Diego |

## Yuzuru Yamakage

Industrial Application of TDA-ML technology: Achievement so far and expectations of future |

As DX (Digital Transformation) has been becoming a big key word among almost all industrial players, AI practitioners got many chances to tackle more complex data, which they’ve not met before. Topological Data Analysis has been recently attracting attention of AI practitioners/Data scientists. Because, TDA would have a great potential to extract hidden features, which current technologies have not successfully found, from complex data by combining with ML technologies. In this session, I present several industrial use cases of TDA-ML and show TDA-ML capability, which would provide great benefit to DX industries. |

Affiliation |
Fujitsu Ltd. |

Biography |
Yuzuru Yamakage received his Ph.D. in 1997 from Tohoku University. He then joined Fujitsu Laboratories Ltd. with a focus on Data Analytics Technology. In 2015, he moved to the AI Service Business Unit at Fujitsu Ltd. and became the Director of the AI Service Dept. of the Software Technology Business Unit of Fujitsu Ltd. in 2020. |