Geometry and Topology of Data
(December 11 - 13, 2017)

Description

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, combinatorial 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 (dsi.brown.edu), and is run in collaboration with ICERM.

Organizing Committee


= speaker    = poster presenter

Monday December 11, 2017
Time Description Speaker Location Abstracts Slides
8:30 - 8:55Registration121 South Main Street Providence RI 11th Floor Collaborative Space
8:55 - 9:00WelcomeICERM Director11th Floor Lecture Hall
9:00 - 9:40From RNA-seq time series data to models of regulatory networksKonstantin Mischaikow, Rutgers University11th Floor Lecture Hall
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9:45 - 10:25Transferring diffusion based manifold learning to trajectories, time varying data, and geometric deep learningMatthew Hirn, Michigan State University11th Floor Lecture Hall
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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 invarianceYannis Kevrekidis, Johns Hopkins University11th Floor Lecture Hall
11:45 - 12:25Spatiotemporal pattern extraction by spectral analysis of vector-valued observablesDimitris Giannakis, New York University11th Floor Lecture Hall
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12:30 - 2:00Break for Lunch / Free Time
2:00 - 2:40Sparse Cech filtrations, persistent cohomology and projective coordinatesJose Perea, Michigan State University11th Floor Lecture Hall
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2:45 - 3:25Learning geometries and analysis of data matrices, and tensors.Ronald Coifman, Yale University11th Floor Lecture Hall
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3:30 - 4:00Coffee/Tea Break 11th Floor Collaborative Space
4:00 - 4:40Analysis of dynamic networks via persistent homologyFacundo Memoli, The Ohio State University11th Floor Lecture Hall
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4:45 - 6:15Welcome Reception11th Floor Collaborative Space

Tuesday December 12, 2017
Time Description Speaker Location Abstracts Slides
9:00 - 9:40Towards homotopical foundations for topological data analysisAndrew Blumberg, University of Texas11th Floor Lecture Hall
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9:45 - 10:25Functional Data Analysis using a Topological Summary Statistic- the Smooth Euler Characteristic TransformLorin Crawford, Brown University11th Floor Lecture Hall
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10:30 - 11:00Coffee/Tea Break 11th Floor Collaborative Space
11:00 - 11:40Persistence Landscapes and the Geometry of DataPeter Bubenik, University of Florida11th Floor Lecture Hall
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11:45 - 12:25Mapping the Space of Molecular Conformations using Cryo-Electron MicroscopesRoy Lederman, Princeton University11th Floor Lecture Hall
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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 actionsSayan Mukherjee, Duke University11th Floor Lecture Hall
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2:45 - 3:25Topology-based image analysis with discrete gradientsAttila Gyulassy, SCI Institute, University of Utah11th Floor Lecture Hall
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3:30 - 4:00Coffee/Tea Break 11th Floor Collaborative Space
4:00 - 4:40Inverse problems in TDA --- focus on metric graphsSteve Oudot, Inria11th Floor Lecture Hall
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Wednesday December 13, 2017
Time Description Speaker Location Abstracts Slides
9:00 - 9:40Comparing shapes of genus zeroJoel Hass, UC Davis11th Floor Lecture Hall
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10:00 - 10:30Coffee/Tea Break 11th Floor Collaborative Space
10:30 - 11:10Approximating Continuous Functions on Persistence Diagrams for Machine Learning TasksElizabeth Munch, Michigan State University11th Floor Lecture Hall
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11:20 - 12:00Fast Deformable Image RegistrationMarc Niethammer, University of North Carolina at Chapel Hill11th Floor Lecture Hall
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12:00 - 1:30Working LunchJeff Brock, DSI Director - Brown University
1:30 - 2:10Studying complicated fluid flows using topological data analysisRachel Levanger, University of Pennsylvania11th Floor Lecture Hall
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2:20 - 3:00Tropical Sufficient Statistics for Persistent HomologySara Kalisnik Verovsek, Max Planck Institute for Mathematics in the Sciences11th Floor Lecture Hall
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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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