Location
This workshop was held at SAMSI.
Description
Topological Data Analysis began a little more than 20 years ago with the introduction of persistence by Edelsbrunner, Lestcher and Zomorodian. Since that time the field has grown significantly. Many strong theorems, numerous algorithms, and pieces of software have been created in that period. More recently, the field has considered stochastic modeling and analysis, which has resulted in interactions with Statistics, Probability, and Computer Science. This workshop focused on the interaction of Statistics and Probability with this new area of Applied Mathematics. The goals were to familiarize people in both areas with techniques from the other and to understand what future directions are the most promising.
Topics included:
- Statistics and persistent homology
- Topological data analysis and inference in dynamical systems and time series
- Topological data analysis and shape statistics
- Topological data analysis and network models
- Probability models for random topology objects
- Statistical applications of Hodge theory
Schedule and Supporting Media
Participant List
Speaker Title and Abstracts
Poster Titles
Monday, February 3, 2014
at SAMSI, Room 150
Time | Description | Speaker | Slides | Videos |
---|---|---|---|---|
8:30-8:55 | Registration | |||
8:55-9:00 | Welcome | |||
9:00-9:40 | Stability and Convergence Properties of Persistence Diagrams in Topological Data Analysis | Frederic Chazal, INRIA | ||
9:40-10:00 | Break | |||
10:00-10:40 | Data Sparsification in Inferring Topology of Manifolds | Yusu Wang, Ohio State University | ||
10:40-11:00 | Break | |||
11:00-11:40 | Statistical Topological Data Analysis using Persistence Landscapes | Peter Bubenik, Cleveland State University | ||
11:40-1:00 | Lunch (provided at SAMSI) | |||
1:00-1:40 | Mean and Variance of Metric Trees | Megan Owen, Lehman College (CUNY) | ||
1:40-2:00 | Break | |||
2:00-2:40 | Some Uniformity Results for Dynamical Systems | Andrew Nobel, University of North Carolina | ||
2:40-3:00 | Break | |||
3:00-3:40 | Statistical Inference for Functional Summaries of Persistent Homology | Larry Wasserman, Carnegie Mellon University | ||
3:40-4:00 | Break | |||
4:00-5:00 | Discussion |
Tuesday, February 4, 2014
at SAMSI, Room 150
Time | Description | Speaker | Slides | Videos |
---|---|---|---|---|
9:00-9:40 | What is the Dimension of the Internet? | Yuliy Baryshnikov, University of Illinois | ||
9:40-10:00 | Break | |||
10:00-10:40 | Can Topological Summary Statistics be Sufficient? | Katharine Turner, University of Chicago | ||
10:40-11:00 | Break | |||
11:00-11:40 | Topological and Statistical Data Analysis | Giseon Heo, University of Alberta | ||
11:40-1:00 | Lunch (provided at SAMSI) | |||
1:00-1:40 | Curvature Sets over Persistence Diagrams | Facundo Memoli, Ohio State University | ||
1:40-2:00 | Break | |||
2:00-2:40 | Persistent Local Homology: Theory, Algorithms, Applications, New Directions | Paul Bendich, Duke University | ||
2:40-3:00 | Break | |||
3:00-3:40 | Hodge Theory in Data Analysis | Lek-Heng Lim, University of Chicago | ||
3:40-4:00 | Break | |||
4:00-5:00 | Discussion | |||
5:00-6:30 | Poster Session and Reception |
Wednesday, February 5, 2014
at SAMSI, Room 150
Time | Description | Speaker | Slides | Videos |
---|---|---|---|---|
9:00-9:40 | Statistical Inference for Persistence Diagrams | Fabrizio Lecci, Carnegie Mellon University | ||
9:40-10:00 | Break | |||
10:00-10:40 | Categorification of Reeb Graphs | Elizabeth Munch, Institute for Mathematics and its Applications | ||
10:40-11:00 | Break | |||
11:00-11:40 | OODA of Tree-Structured Data Objects | J.S. Marron, University of North Carolina | ||
11:40-12:00 | Discussion | |||
12:00 | Box Lunch (provided at SAMSI) – Free Afternoon |
Thursday, February 6, 2014
at SAMSI, Room 150
Time | Description | Speaker | Slides | Videos |
---|---|---|---|---|
9:00-9:40 | Persistent Homology of Time-delay Embeddings | Jose Perea, Duke University | ||
9:40-10:00 | Break | |||
10:00-10:40 | Persistent Homology of the Intergalactic Medium via the Lyman-alpha Forest | Jessi Cisewski, Carnegie Mellon University | ||
10:40-11:00 | Break | |||
11:00-11:40 | Geometric Inference on Kernel Density Estimates | Bei Wang, University of Utah | ||
11:40-1:00 | Lunch (provided at SAMSI) | |||
1:00-1:40 | Local Homology Based Distance Between Maps | Brittany Fasy, Tulane University | ||
1:40-2:00 | Break | |||
2:00-2:40 | Distributed Homology using Harmonics | Harish Chintakunta, North Carolina State University | ||
2:40-3:00 | Break | |||
3:00-3:40 | Neighborhood Hypothesis Testing for Mean Contour Shapes of Corpus Callosum Mid Sections | Vic Patrangenaru, Florida State University | ||
3:40-4:00 | Break | |||
4:00-5:00 | Discussion |
Friday, February 7, 2014
at SAMSI, Room 150
Time | Description | Speaker | Slides | Videos |
---|---|---|---|---|
9:00-9:40 | Phase Transitions in Random Čech Complexes | Omer Bobrowski, Duke University | ||
9:40-10:00 | Break | |||
10:00-10:40 | Quantifying Coverage in Dynamic Sensor Networks with Zigzag Persistent Homology | Jennifer Gamble, North Carolina State University | ||
10:40-11:00 | Break | |||
11:00-11:40 | Pyrosequencing and Computational Topology: A tale of two homologies | Peter Kim, University of Guelph | ||
11:40-12:00 | Discussion | |||
12:00 | Lunch (provided at SAMSI) Adjourn |