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.

This workshop is part of the Brown Data Science Initiative project, funded by the National Science Foundation's TRIPODS program.

Image for "Geometry and Topology of Data"
This workshop is part of the Brown Data Science Initiative project, funded by the National Science Foundation's TRIPODS program.

Confirmed Speakers & Participants

Talks will be presented virtually or in-person as indicated in the schedule below.

  • Speaker
  • Poster Presenter
  • Attendee
  • Virtual Attendee

Workshop Schedule

Monday, December 11, 2017
TimeEventLocationMaterials
8:30 - 8:55am ESTRegistration121 South Main Street Providence RI 11th Floor Collaborative Space 
8:55 - 9:00am ESTWelcome - ICERM Director11th Floor Lecture Hall 
9:00 - 9:40am ESTFrom RNA-seq time series data to models of regulatory networks - Konstantin Mischaikow, Rutgers University11th Floor Lecture Hall
9:45 - 10:25am ESTTransferring diffusion based manifold learning to trajectories, time varying data, and geometric deep learning - Matthew Hirn, Michigan State University11th Floor Lecture Hall
10:30 - 11:00am ESTCoffee/Tea Break 11th Floor Collaborative Space 
11:00 - 11:40am ESTNo space, no time: data, equal space and some thoughts on gauge invariance - Yannis Kevrekidis, Johns Hopkins University11th Floor Lecture Hall 
11:45 - 12:25pm ESTSpatiotemporal pattern extraction by spectral analysis of vector-valued observables - Dimitris Giannakis, New York University11th Floor Lecture Hall
12:30 - 2:00pm ESTBreak for Lunch / Free Time  
2:00 - 2:40pm ESTSparse Cech filtrations, persistent cohomology and projective coordinates - Jose Perea, Michigan State University11th Floor Lecture Hall
2:45 - 3:25pm ESTLearning geometries and analysis of data matrices, and tensors. - Ronald Coifman, Yale University11th Floor Lecture Hall
3:30 - 4:00pm ESTCoffee/Tea Break 11th Floor Collaborative Space 
4:00 - 4:40pm ESTAnalysis of dynamic networks via persistent homology - Facundo Memoli, The Ohio State University11th Floor Lecture Hall
4:45 - 6:15pm ESTWelcome Reception11th Floor Collaborative Space 
Tuesday, December 12, 2017
TimeEventLocationMaterials
9:00 - 9:40am ESTTowards homotopical foundations for topological data analysis - Andrew Blumberg, University of Texas11th Floor Lecture Hall
9:45 - 10:25am ESTFunctional Data Analysis using a Topological Summary Statistic- the Smooth Euler Characteristic Transform - Lorin Crawford, Brown University11th Floor Lecture Hall
10:30 - 11:00am ESTCoffee/Tea Break 11th Floor Collaborative Space 
11:00 - 11:40am ESTPersistence Landscapes and the Geometry of Data - Peter Bubenik, University of Florida11th Floor Lecture Hall
11:45 - 12:25pm ESTMapping the Space of Molecular Conformations using Cryo-Electron Microscopes - Roy Lederman, Princeton University11th Floor Lecture Hall
12:30 - 12:40pm ESTWorkshop Group Photo11th Floor Lecture Hall 
12:40 - 2:00pm ESTBreak for Lunch / Free Time  
2:00 - 2:40pm ESTInference in dynamical systems and the geometry of learning group actions - Sayan Mukherjee, Duke University11th Floor Lecture Hall
2:45 - 3:25pm ESTTopology-based image analysis with discrete gradients - Attila Gyulassy, SCI Institute, University of Utah11th Floor Lecture Hall
3:30 - 4:00pm ESTCoffee/Tea Break 11th Floor Collaborative Space 
4:00 - 4:40pm ESTInverse problems in TDA --- focus on metric graphs - Steve Oudot, Inria11th Floor Lecture Hall
Wednesday, December 13, 2017
TimeEventLocationMaterials
9:00 - 9:40am ESTComparing shapes of genus zero - Joel Hass, UC Davis11th Floor Lecture Hall
10:00 - 10:30am ESTCoffee/Tea Break 11th Floor Collaborative Space 
10:30 - 11:10am ESTApproximating Continuous Functions on Persistence Diagrams for Machine Learning Tasks - Elizabeth Munch, Michigan State University11th Floor Lecture Hall
11:20 - 12:00pm ESTFast Deformable Image Registration - Marc Niethammer, University of North Carolina at Chapel Hill11th Floor Lecture Hall
12:00 - 1:30pm ESTWorking Lunch - Jeff Brock, DSI Director - Brown University  
1:30 - 2:10pm ESTStudying complicated fluid flows using topological data analysis - Rachel Levanger, University of Pennsylvania11th Floor Lecture Hall
2:20 - 3:00pm ESTTropical Sufficient Statistics for Persistent Homology - Sara Kalisnik Verovsek, Max Planck Institute for Mathematics in the Sciences11th Floor Lecture Hall
3:10 - 3:30pm ESTCoffee/Tea Break 11th Floor Collaborative Space 
3:30 - 4:10pm ESTDirected complexes, non-linear rank and convex sensing. - Vladimir Itskov, Penn State11th Floor Lecture Hall

Lecture Videos

Directed complexes, non-linear rank and convex sensing

Vladimir Itskov
The Pennsylvania State University
December 13, 2017
Geometry and Topology of Data
Play     Abstract

Studying complicated fluid flows using topological data analysis

Rachel Levanger
University of Pennsylvania
December 13, 2017
Geometry and Topology of Data
Play     Abstract

Approximating Continuous Functions on Persistence Diagrams for Machine Learning Tasks

Elizabeth Munch
Michigan State University
December 13, 2017
Geometry and Topology of Data
Play     Abstract

Inverse problems in TDA --- focus on metric graphs

Steve Oudot
Inria
December 12, 2017
Geometry and Topology of Data
Play     Abstract     Slides

Topology-based image analysis with discrete gradients

Attila Gyulassy
University of Utah
December 12, 2017
Geometry and Topology of Data
Play     Abstract

Inference in dynamical systems and the geometry of learning group actions

Sayan Mukherjee
Duke University
December 12, 2017
Geometry and Topology of Data
Play     Abstract     Slides

Persistence Landscapes and the Geometry of Data

Peter Bubenik
University of Florida
December 12, 2017
Geometry and Topology of Data
Play     Abstract     Slides

Functional Data Analysis using a Topological Summary Statistic- the Smooth Euler Characteristic Transform

Lorin Crawford
Brown University
December 12, 2017
Geometry and Topology of Data
Play     Abstract     Slides

Analysis of dynamic networks via persistent homology

Facundo Memoli
The Ohio State University
December 11, 2017
Geometry and Topology of Data
Play     Abstract

Learning geometries and analysis of data matrices, and tensors

Raphy Coifman
Yale University
December 11, 2017
Geometry and Topology of Data
Play     Abstract

Sparse Cech filtrations, persistent cohomology and projective coordinates

Jose Perea
Michigan State University
December 11, 2017
Geometry and Topology of Data
Play     Abstract

Spatiotemporal pattern extraction by spectral analysis of vector-valued observables

Dimitris Giannakis
New York University
December 11, 2017
Geometry and Topology of Data
Play     Abstract     Slides

Transferring Diffusion Based Manifold Learning to Trajectories, Time Varying Data, and Geometric Deep Learning

Matthew Hirn
Michigan State University
December 11, 2017
Geometry and Topology of Data
Play     Abstract     Slides

From RNA-seq time series data to models of regulatory networks

Konstantin Mischaikow
Rutgers University
December 11, 2017
Geometry and Topology of Data
Play     Abstract     Slides