Organizing Committee
Abstract

The scale, dimensionality, and complexity of large data has given rise to new topological and geometric methods for understanding what features in a data set are robust under perturbations of the system. Tools from algebraic topology and coarse geometry have been brought fruitfully to bear in a number of contexts leading to a surge of interest in persistent homology, combintorial geometry, and discrete Morse theory.

Likewise, new frameworks have emerged from harmonic analysis to develop diffusion geometries for large data, enabling multi-scale analyses, and other dynamical approaches to understanding complex data sets. Tools for enabling visualization of each of these methods are in development and increasingly granting researchers the ability to understand their data in new ways.

This workshop will bring together a broad range of researchers for a short workshop to attempt to set directions for future research. This workshop is part of the Brown Data Science Initiative's new NSF TRIPODS grant, and is run in collaboration with ICERM.

Confirmed Speakers & Participants

Workshop Schedule

Monday, December 11, 2017
TimeEventLocationMaterials
8:30 - 8:55Registration121 South Main Street Providence RI 11th Floor Collaborative Space 
8:55 - 9:00Welcome - ICERM Director11th Floor Lecture Hall 
9:00 - 9:40From RNA-seq time series data to models of regulatory networks - Konstantin Mischaikow, Rutgers University11th Floor Lecture Hall
9:45 - 10:25Transferring diffusion based manifold learning to trajectories, time varying data, and geometric deep learning - Matthew Hirn, Michigan State University11th Floor Lecture Hall
10:30 - 11:00Coffee/Tea Break 11th Floor Collaborative Space 
11:00 - 11:40No space, no time: data, equal space and some thoughts on gauge invariance - Yannis Kevrekidis, Johns Hopkins University11th Floor Lecture Hall 
11:45 - 12:25Spatiotemporal pattern extraction by spectral analysis of vector-valued observables - Dimitris Giannakis, New York University11th Floor Lecture Hall
12:30 - 2:00Break for Lunch / Free Time  
2:00 - 2:40Sparse Cech filtrations, persistent cohomology and projective coordinates - Jose Perea, Michigan State University11th Floor Lecture Hall
2:45 - 3:25Learning geometries and analysis of data matrices, and tensors. - Ronald Coifman, Yale University11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break 11th Floor Collaborative Space 
4:00 - 4:40Analysis of dynamic networks via persistent homology - Facundo Memoli, The Ohio State University11th Floor Lecture Hall
4:45 - 6:15Welcome Reception11th Floor Collaborative Space 
Tuesday, December 12, 2017
TimeEventLocationMaterials
9:00 - 9:40Towards homotopical foundations for topological data analysis - Andrew Blumberg, University of Texas11th Floor Lecture Hall
9:45 - 10:25Functional Data Analysis using a Topological Summary Statistic- the Smooth Euler Characteristic Transform - Lorin Crawford, Brown University11th Floor Lecture Hall
10:30 - 11:00Coffee/Tea Break 11th Floor Collaborative Space 
11:00 - 11:40Persistence Landscapes and the Geometry of Data - Peter Bubenik, University of Florida11th Floor Lecture Hall
11:45 - 12:25Mapping the Space of Molecular Conformations using Cryo-Electron Microscopes - Roy Lederman, Princeton University11th Floor Lecture Hall
12:30 - 12:40Workshop Group Photo11th Floor Lecture Hall 
12:40 - 2:00Break for Lunch / Free Time  
2:00 - 2:40Inference in dynamical systems and the geometry of learning group actions - Sayan Mukherjee, Duke University11th Floor Lecture Hall
2:45 - 3:25Topology-based image analysis with discrete gradients - Attila Gyulassy, SCI Institute, University of Utah11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break 11th Floor Collaborative Space 
4:00 - 4:40Inverse problems in TDA --- focus on metric graphs - Steve Oudot, Inria11th Floor Lecture Hall
Wednesday, December 13, 2017
TimeEventLocationMaterials
9:00 - 9:40Comparing shapes of genus zero - Joel Hass, UC Davis11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break 11th Floor Collaborative Space 
10:30 - 11:10Approximating Continuous Functions on Persistence Diagrams for Machine Learning Tasks - Elizabeth Munch, Michigan State University11th Floor Lecture Hall
11:20 - 12:00Fast Deformable Image Registration - Marc Niethammer, University of North Carolina at Chapel Hill11th Floor Lecture Hall
12:00 - 1:30Working Lunch - Jeff Brock, DSI Director - Brown University  
1:30 - 2:10Studying complicated fluid flows using topological data analysis - Rachel Levanger, University of Pennsylvania11th Floor Lecture Hall
2:20 - 3:00Tropical Sufficient Statistics for Persistent Homology - Sara Kalisnik Verovsek, Max Planck Institute for Mathematics in the Sciences11th Floor Lecture Hall
3:10 - 3:30Coffee/Tea Break 11th Floor Collaborative Space 
3:30 - 4:10Directed complexes, non-linear rank and convex sensing. - Vladimir Itskov, Penn State11th Floor Lecture Hall

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Submissions must be received within 30 days of ICERM departure to avoid applicable taxes. Submissions after thirty days will incur applicable taxes. No submissions are accepted more than six months after the program end.

Lecture Videos

Topology-based image analysis with discrete gradients

Attila Gyulassy
SCI Institute, University of Utah
December 12, 2017

Persistence Landscapes and the Geometry of Data

Peter Bubenik
University of Florida
December 12, 2017

Analysis of dynamic networks via persistent homology

Facundo Memoli
The Ohio State University
December 11, 2017